Best approximation in spaces of bounded linear operators

Grzegorz Lewicki

Best approximation in spaces of bounded linear operators

Grzegorz Lewicki

Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1994

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CONTENTSChapter 0...............................................................................................................................................................................5 0.1. Introduction..................................................................................................................................................................5 0.2. Preliminary results.......................................................................................................................................................9Chapter I..............................................................................................................................................................................16 I.1. Best approximation in finite-dimensional subspaces of ℒ(B,D)....................................................................................16 I.2. Kolmogorov’s type criteria for spaces of compact operators; general case.................................................................26 I.3. Criteria for the space

K (C_{K} (T))

.............................................................................................................................30 I.4. The case of sequence spaces....................................................................................................................................38Chapter II.............................................................................................................................................................................43 II.1. Extensions of linear operators from hyperplanes of

l_{\infty}^{(n)}

.................................................................................43 II.2. Minimal projections onto hyperplanes of

l_{1}^{(n)}

...................................................................................................52 II.3. Strongly unique minimal projections onto hyperplanes of

l_{\infty}^{(n)}

and

l_{1}^{(n)}

...............................................59 II.4. Minimal projections onto subspaces of

l_{\infty}^{(n)}

of codimension two......................................................................71 II.5. Uniqueness of minimal projections onto subspace of

l_{\infty}^{(n)}

of codimension two................................................75 II.6. Strong unicity criterion in some space of operators....................................................................................................79Chapter III.............................................................................................................................................................................83 III.1. Extensions of linear operators from finite-dimensional subspaces I...........................................................................83 III.2. Extensions of linear operators from finite-dimensional subspaces II..........................................................................90 III.3. Algorithms for seeking the constant

W_{m}

..............................................................................................................97References..........................................................................................................................................................................99Index..................................................................................................................................................................................102Index of symbols................................................................................................................................................................1021991 Mathematics Subject Classification: 41A35, 41A52, 41A65, 46B99, 47A30.

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Grzegorz Lewicki. Best approximation in spaces of bounded linear operators. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1994. <http://eudml.org/doc/268573>.

@book{GrzegorzLewicki1994,
abstract = {CONTENTSChapter 0...............................................................................................................................................................................5 0.1. Introduction..................................................................................................................................................................5 0.2. Preliminary results.......................................................................................................................................................9Chapter I..............................................................................................................................................................................16 I.1. Best approximation in finite-dimensional subspaces of ℒ(B,D)....................................................................................16 I.2. Kolmogorov’s type criteria for spaces of compact operators; general case.................................................................26 I.3. Criteria for the space $K(C_K(T))$.............................................................................................................................30 I.4. The case of sequence spaces....................................................................................................................................38Chapter II.............................................................................................................................................................................43 II.1. Extensions of linear operators from hyperplanes of $l^\{(n)\}_∞$.................................................................................43 II.2. Minimal projections onto hyperplanes of $l^\{(n)\}_1$...................................................................................................52 II.3. Strongly unique minimal projections onto hyperplanes of $l^\{(n)\}_∞$ and $l^\{(n)\}_1$...............................................59 II.4. Minimal projections onto subspaces of $l^\{(n)\}_∞$ of codimension two......................................................................71 II.5. Uniqueness of minimal projections onto subspace of $l^\{(n)\}_∞$ of codimension two................................................75 II.6. Strong unicity criterion in some space of operators....................................................................................................79Chapter III.............................................................................................................................................................................83 III.1. Extensions of linear operators from finite-dimensional subspaces I...........................................................................83 III.2. Extensions of linear operators from finite-dimensional subspaces II..........................................................................90 III.3. Algorithms for seeking the constant $W_m$..............................................................................................................97References..........................................................................................................................................................................99Index..................................................................................................................................................................................102Index of symbols................................................................................................................................................................1021991 Mathematics Subject Classification: 41A35, 41A52, 41A65, 46B99, 47A30.},
author = {Grzegorz Lewicki},
keywords = {best approximation; linear operators; compact operators; minimal projections; Kolmogorov's criterion; strongly unique best approximation},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Best approximation in spaces of bounded linear operators},
url = {http://eudml.org/doc/268573},
year = {1994},
}

TY - BOOK
AU - Grzegorz Lewicki
TI - Best approximation in spaces of bounded linear operators
PY - 1994
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSChapter 0...............................................................................................................................................................................5 0.1. Introduction..................................................................................................................................................................5 0.2. Preliminary results.......................................................................................................................................................9Chapter I..............................................................................................................................................................................16 I.1. Best approximation in finite-dimensional subspaces of ℒ(B,D)....................................................................................16 I.2. Kolmogorov’s type criteria for spaces of compact operators; general case.................................................................26 I.3. Criteria for the space $K(C_K(T))$.............................................................................................................................30 I.4. The case of sequence spaces....................................................................................................................................38Chapter II.............................................................................................................................................................................43 II.1. Extensions of linear operators from hyperplanes of $l^{(n)}_∞$.................................................................................43 II.2. Minimal projections onto hyperplanes of $l^{(n)}_1$...................................................................................................52 II.3. Strongly unique minimal projections onto hyperplanes of $l^{(n)}_∞$ and $l^{(n)}_1$...............................................59 II.4. Minimal projections onto subspaces of $l^{(n)}_∞$ of codimension two......................................................................71 II.5. Uniqueness of minimal projections onto subspace of $l^{(n)}_∞$ of codimension two................................................75 II.6. Strong unicity criterion in some space of operators....................................................................................................79Chapter III.............................................................................................................................................................................83 III.1. Extensions of linear operators from finite-dimensional subspaces I...........................................................................83 III.2. Extensions of linear operators from finite-dimensional subspaces II..........................................................................90 III.3. Algorithms for seeking the constant $W_m$..............................................................................................................97References..........................................................................................................................................................................99Index..................................................................................................................................................................................102Index of symbols................................................................................................................................................................1021991 Mathematics Subject Classification: 41A35, 41A52, 41A65, 46B99, 47A30.
LA - eng
KW - best approximation; linear operators; compact operators; minimal projections; Kolmogorov's criterion; strongly unique best approximation
UR - http://eudml.org/doc/268573
ER -

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