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Best approximation in spaces of bounded linear operators

100%

Lewicki G.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Chapter 0...............................................................................................................................................................................5 0.1. Introduction..................................................................................................................................................................5 0.2. Preliminary results.......................................................................................................................................................9 Chapter 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....................................................................................................................................38 Chapter 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....................................................................................................79 Chapter 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 $W_m$..............................................................................................................97 References..........................................................................................................................................................................99 Index..................................................................................................................................................................................102 Index of symbols................................................................................................................................................................102

$I$-sets and cominimal projections

98%

Lipieta A.

Commentationes Mathematicae

2006

tom 46

nr 1

Let $Y \subset l^n_\infty$ be a subspace of codimension two. For $n = 4$ the formula for cominimal projections will be presented. For $n = 5$ the complete characterization of $I$-sets which determined cominimal projections and consequently the manner of finding cominimal projections will be given. This completes the results from [15].

Ograniczanie wyników

1 Commentationes Mathematicae

1 Lewicki G.

1 Lipieta A.

1 2006

1 1994

Wyniki wyszukiwania

Best approximation in spaces of bounded linear operators

\(I\)-sets and cominimal projections