# Structure properties of D-R spaces

• Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1981

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## Abstract

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CONTENTSIntroduction................................................................................................................................... 5 Notations.......................................................................................................................... 5§ 1. Preliminaries........................................................................................................................ 6 1. Right invertible operators.................................................................................................. 6 2. D-R vector spaces.............................................................................................................. 7 3. Basic types of D-R spaces............................................................................................... 7  3.1. Examples............................................................................................................. 7 4. Subspaces.......................................................................................................................... 8 5. Homomorphisms............................................................................................................... 8  5.1 Quotient spaces and homomorphisms......................................................... 10§2. The general Taylor theorem............................................................................................... 11 1. The elementary Taylor theorem....................................................................................... 11  1.1. Bands of subspaces....................................................................................... 12 2. The general Taylor theorem............................................................................................. 14§ 3. Structure elements of D-R spaces................................................................................... 17 1. The simple Taylor formula................................................................................................ 17 2. Distinguished subspaces and subspace chains....................................................... 18  2.1. Canonical subspaces of a D-R space........................................................ 18  2.2. The space ${D}_{i}$............................................................................................. 19  2.3. The space S...................................................................................................... 19  2.4. The space Q..................................................................................................... 20 3. Extension of the domain of D........................................................................................... 21 4. The structure chain............................................................................................................ 22 5. Components and formal component series................................................................ 23 6. Examples............................................................................................................................. 25§ 4. The D-R homomorphism theorem.................................................................................. 27 1. The D-R reference space ${X}_{0}$..................................................................................... 27  1.1. X(Z) as a ${D}_{0}-{R}_{0}$ space with ${D}_{D}0$ = X(Z)................................... 28  1.2. The ${d}_{0}$-convergence................................................................................ 28  1.3. The Volterra property of ${X}_{0}$ and eigenspaces of ${D}_{0}$...................... 31 2. ${D}_{D}0$${X}_{0}\left(Z\right)$.......................................................................... 32 3. The D-R homomorphism theorem................................................................................. 33  3.1. Eigenvectors of D and R................................................................................. 35 4. The D-R homomorphism theorem for ${D}_{D}0$ X.................. 35 5. ${d}_{0}$-topology................................................................................................................... 38

## How to cite

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Hartmut von Trotha. Structure properties of D-R spaces. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1981. <http://eudml.org/doc/268475>.

@book{HartmutvonTrotha1981,
abstract = {CONTENTSIntroduction................................................................................................................................... 5 Notations.......................................................................................................................... 5§ 1. Preliminaries........................................................................................................................ 6 1. Right invertible operators.................................................................................................. 6 2. D-R vector spaces.............................................................................................................. 7 3. Basic types of D-R spaces............................................................................................... 7  3.1. Examples............................................................................................................. 7 4. Subspaces.......................................................................................................................... 8 5. Homomorphisms............................................................................................................... 8  5.1 Quotient spaces and homomorphisms......................................................... 10§2. The general Taylor theorem............................................................................................... 11 1. The elementary Taylor theorem....................................................................................... 11  1.1. Bands of subspaces....................................................................................... 12 2. The general Taylor theorem............................................................................................. 14§ 3. Structure elements of D-R spaces................................................................................... 17 1. The simple Taylor formula................................................................................................ 17 2. Distinguished subspaces and subspace chains....................................................... 18  2.1. Canonical subspaces of a D-R space........................................................ 18  2.2. The space $D_i$............................................................................................. 19  2.3. The space S...................................................................................................... 19  2.4. The space Q..................................................................................................... 20 3. Extension of the domain of D........................................................................................... 21 4. The structure chain............................................................................................................ 22 5. Components and formal component series................................................................ 23 6. Examples............................................................................................................................. 25§ 4. The D-R homomorphism theorem.................................................................................. 27 1. The D-R reference space $X_0$..................................................................................... 27  1.1. X(Z) as a $D_0-R_0$ space with $D_D_0$ = X(Z)................................... 28  1.2. The $d_0$-convergence................................................................................ 28  1.3. The Volterra property of $X_0$ and eigenspaces of $D_0$...................... 31 2. $D_D_0$$\UnimplementedOperator$$X_0(Z)$.......................................................................... 32 3. The D-R homomorphism theorem................................................................................. 33  3.1. Eigenvectors of D and R................................................................................. 35 4. The D-R homomorphism theorem for $D_D_0$$\UnimplementedOperator X.................. 35 5. d_0-topology................................................................................................................... 38}, author = {Hartmut von Trotha}, keywords = {linear spaces with right invertible operators; D-R space; reference space}, language = {eng}, location = {Warszawa}, publisher = {Instytut Matematyczny Polskiej Akademi Nauk}, title = {Structure properties of D-R spaces}, url = {http://eudml.org/doc/268475}, year = {1981}, } TY - BOOK AU - Hartmut von Trotha TI - Structure properties of D-R spaces PY - 1981 CY - Warszawa PB - Instytut Matematyczny Polskiej Akademi Nauk AB - CONTENTSIntroduction................................................................................................................................... 5 Notations.......................................................................................................................... 5§ 1. Preliminaries........................................................................................................................ 6 1. Right invertible operators.................................................................................................. 6 2. D-R vector spaces.............................................................................................................. 7 3. Basic types of D-R spaces............................................................................................... 7 3.1. Examples............................................................................................................. 7 4. Subspaces.......................................................................................................................... 8 5. Homomorphisms............................................................................................................... 8 5.1 Quotient spaces and homomorphisms......................................................... 10§2. The general Taylor theorem............................................................................................... 11 1. The elementary Taylor theorem....................................................................................... 11 1.1. Bands of subspaces....................................................................................... 12 2. The general Taylor theorem............................................................................................. 14§ 3. Structure elements of D-R spaces................................................................................... 17 1. The simple Taylor formula................................................................................................ 17 2. Distinguished subspaces and subspace chains....................................................... 18 2.1. Canonical subspaces of a D-R space........................................................ 18 2.2. The space D_i............................................................................................. 19 2.3. The space S...................................................................................................... 19 2.4. The space Q..................................................................................................... 20 3. Extension of the domain of D........................................................................................... 21 4. The structure chain............................................................................................................ 22 5. Components and formal component series................................................................ 23 6. Examples............................................................................................................................. 25§ 4. The D-R homomorphism theorem.................................................................................. 27 1. The D-R reference space X_0..................................................................................... 27 1.1. X(Z) as a D_0-R_0 space with D_D_0 = X(Z)................................... 28 1.2. The d_0-convergence................................................................................ 28 1.3. The Volterra property of X_0 and eigenspaces of D_0...................... 31 2. D_D_0$$\UnimplementedOperator $$X_0(Z).......................................................................... 32 3. The D-R homomorphism theorem................................................................................. 33 3.1. Eigenvectors of D and R................................................................................. 35 4. The D-R homomorphism theorem for D_D_0$$\UnimplementedOperator$ X.................. 35 5. $d_0$-topology................................................................................................................... 38
LA - eng
KW - linear spaces with right invertible operators; D-R space; reference space
UR - http://eudml.org/doc/268475
ER -

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