Best approximation in spaces of bounded linear operators

Grzegorz Lewicki

GDML_Books, (1994), p.

Résumé

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................................................................................................................................................................102

1991 Mathematics Subject Classification: 41A35, 41A52, 41A65, 46B99, 47A30.

Détail

Zbl 0826.41025

EUDML-ID : urn:eudml:doc:268573