On isomorphic classification of tensor products $E_{\infty }\left(a\right)\otimes ̂E_{\infty }^{\text{'}}\left(b\right)$

Goncharov A., Zahariuta V., and Terzioğlu Tosun. On isomorphic classification of tensor products $E_{∞}(a) ⊗̂ E^{\prime }_{∞}(b)$. 1996. <http://eudml.org/doc/275828>.

@book{GoncharovA1996,
abstract = {Abstract New linear topological invariants are introduced and utilized to give an isomorphic classification of tensor products of the type $E_\{∞\}(a) ⊗̂ E^\{\prime \}_\{∞\}(b)$, where $E_\{∞\}(a)$ is a power series space of infinite type. These invariants are modifications of those suggested earlier by Zahariuta. In particular, some new results are obtained for spaces of infinitely differentiable functions with values in a locally convex space X. These spaces coincide, up to isomorphism, with spaces L(s’,X) of all continuous linear operators into X from the dual space of the space s of rapidly decreasing sequences. Most of the results given here with proofs were announced in [12].CONTENTS 0. Introduction...............................................5 1. Preliminaries.............................................6 2. Power series space-valued case..............8 3. Main results..............................................9 4. F- and DF-subspaces.............................11 5. Quasidiagonal isomorphism....................13 6. Sufficiency...............................................14 7. Linear Topological Invariants (LTI)..........16 8. Necessary conditions..............................20 9. Spaces $s ⊗̂ E^\{\prime \}_∞(b)$............................22 10. Spaces $s^\{\prime \} ⊗̂ E_\{∞\}(a)$.......................23 References.................................................261991 Mathematics Subject Classification: 46A04, 46A45, 46A11, 46A32.},
author = {Goncharov A., Zahariuta V., Terzioğlu Tosun},
keywords = {linear topological invariants; isomorphic classification of tensor products; power series space; dual space of the space ; rapidly decreasing sequences},
language = {eng},
title = {On isomorphic classification of tensor products $E_\{∞\}(a) ⊗̂ E^\{\prime \}_\{∞\}(b)$},
url = {http://eudml.org/doc/275828},
year = {1996},
}

TY - BOOK
AU - Goncharov A.
AU - Zahariuta V.
AU - Terzioğlu Tosun
TI - On isomorphic classification of tensor products $E_{∞}(a) ⊗̂ E^{\prime }_{∞}(b)$
PY - 1996
AB - Abstract New linear topological invariants are introduced and utilized to give an isomorphic classification of tensor products of the type $E_{∞}(a) ⊗̂ E^{\prime }_{∞}(b)$, where $E_{∞}(a)$ is a power series space of infinite type. These invariants are modifications of those suggested earlier by Zahariuta. In particular, some new results are obtained for spaces of infinitely differentiable functions with values in a locally convex space X. These spaces coincide, up to isomorphism, with spaces L(s’,X) of all continuous linear operators into X from the dual space of the space s of rapidly decreasing sequences. Most of the results given here with proofs were announced in [12].CONTENTS 0. Introduction...............................................5 1. Preliminaries.............................................6 2. Power series space-valued case..............8 3. Main results..............................................9 4. F- and DF-subspaces.............................11 5. Quasidiagonal isomorphism....................13 6. Sufficiency...............................................14 7. Linear Topological Invariants (LTI)..........16 8. Necessary conditions..............................20 9. Spaces $s ⊗̂ E^{\prime }_∞(b)$............................22 10. Spaces $s^{\prime } ⊗̂ E_{∞}(a)$.......................23 References.................................................261991 Mathematics Subject Classification: 46A04, 46A45, 46A11, 46A32.
LA - eng
KW - linear topological invariants; isomorphic classification of tensor products; power series space; dual space of the space ; rapidly decreasing sequences
UR - http://eudml.org/doc/275828
ER -