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1

Factorization of operators on C*-algebras

100%

Randrianantoanina N.

Studia Mathematica

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1998

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tom 128

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nr 3

273-285

EN

Let A be a C*-algebra. We prove that every absolutely summing operator from A into $ℓ_2$ factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite-dimensional examples that show that one cannot replace the 4-Schatten-von Neumann class by the p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of capacity ε → N(ε) so that if A is a C*-algebra and $T ∈ Π_1(A,ℓ_2)$ with $π_1(T) ≤ 1$, then for every ε >0, the ε-capacity of the image of the unit ball of A under T does not exceed N(ε). This answers positively a question raised by Pełczyński.

2

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Series representation of compact linear operators in Banach spaces

70%

Edmunds D. E., Lang J.

Commentationes Mathematicae

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2016

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tom 56

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nr 1

EN

Let $p\in(1,\infty)$ and $I=(0,1)$; suppose that $T\colon L_{p}(I)\rightarrow L_{p}(I)$ is a~compact linear map with trivial kernel and range dense in $L_{p}(I)$. It is shown that if the Gelfand numbers of $T$ decay sufficiently quickly, then the action of $T$ is given by a series with calculable coefficients. The special properties of $L_{p}(I)$ enable this to be established under weaker conditions on the Gelfand numbers than in earlier work set in the context of more general spaces.

3

Best approximation in spaces of bounded linear operators

62%

Lewicki G.

Instytut Matematyczny Polskiej Akademii Nauk

EN

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

4

Weighted composition operators via Berezin transform and Carleson measure

61%

Kumar R., Singh K. J.

Commentationes Mathematicae

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2006

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tom 46

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nr 1

EN

In this paper, we study the boundedness and the compactness of weighted composition operators on Hardy spaces and weighted Bergman spaces of the unit polydisc in $\mathbf{C}^n$.

Ograniczanie wyników

2 Commentationes Mathematicae

1 Studia Mathematica

1 Edmunds D. E.

1 Kumar R.

1 Lang J.

1 Lewicki G.

1 Randrianantoanina N.

1 Singh K. J.

1 2016

1 2006

1 1998

1 1994

Factorization of operators on C*-algebras

Series representation of compact linear operators in Banach spaces

Best approximation in spaces of bounded linear operators

Weighted composition operators via Berezin transform and Carleson measure