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1
Content available remote

What is "local theory of Banach spaces"?

100%
Pietsch A.
Studia Mathematica
|
1999
|
tom 135
|
nr 3
273-298
EN
Banach space theory splits into several subtheories. On the one hand, there are an isometric and an isomorphic part; on the other hand, we speak of global and local aspects. While the concepts of isometry and isomorphy are clear, everybody seems to have its own interpretation of what "local theory" means. In this essay we analyze this situation and propose rigorous definitions, which are based on new concepts of local representability of operators.
2
Content available remote

Shift-invariant functionals on Banach sequence spaces

100%
Pietsch A.
Studia Mathematica
|
2013
|
tom 214
|
nr 1
37-66
EN
The present paper is a continuation of [23], from which we know that the theory of traces on the Marcinkiewicz operator ideal $𝔐 (H):= {T ∈ 𝔏(H): sup_{1≤m<∞} 1/(log m + 1) ∑_{n=1}^{m} aₙ(T) < ∞}$ can be reduced to the theory of shift-invariant functionals on the Banach sequence space $𝔴(ℕ₀):= {c = (γ_{l}): sup_{0≤k<∞} 1/(k+1) ∑_{l=0}^{k} |γ_{l}| < ∞}$. The final purpose of my studies, which will be finished in [24], is the following. Using the density character as a measure, I want to determine the size of some subspaces of the dual 𝔐 *(H). Of particular interest are the sets formed by the Dixmier traces and the Connes-Dixmier traces (see [2], [4], [6], and [13]). As an intermediate step, the corresponding subspaces of 𝔴*(ℕ₀) are treated. This approach has a significant advantage, since non-commutative problems turn into commutative ones.
3
Content available remote

Bad properties of the Bernstein numbers

100%
Pietsch A.
Studia Mathematica
|
2008
|
tom 184
|
nr 3
263-269
EN
We show that the classes $𝔏_{p}^{bern}: = {T: (bₙ(T) ) ∈ l_{p}}$ associated with the Bernstein numbers bₙ fail to be operator ideals. Moreover, $𝔏_{p}^{bern} ∘ 𝔏_{q}^{bern} ⊈ 𝔏_{r}^{bern}$ for 1/r = 1/p + 1/q.
4
Content available remote

Distirbution of eigenvalues and nuclearity

50%
Pietsch A.
Banach Center Publications
|
1982
|
tom 8
|
nr 1
361-365
5
Content available remote

Interpolationstheorie für Banachideale von beschränkten linearen Operatoren

45%
Pietsch A., Triebel H.
Studia Mathematica
|
1968
|
tom 31
|
nr 1
95-109
6
Content available remote

p-nukleare und p-integrale Abbildungen in Banachräumen

32%
Persson A., Pietsch A.
Studia Mathematica
|
1969
|
tom 33
|
nr 1
19-62
7
Content available remote

Ideale von $S_{p}$-Operatoren in Banachräumen

32%
Pietsch A.
Studia Mathematica
|
1970
|
tom 38
|
nr 1
59-69
8
Content available remote

Type and cotype numbers of operators on Banach spaces

32%
Pietsch A.
Studia Mathematica
|
1990
|
tom 96
|
nr 1
21-37
9
Content available remote

s-Numbers of operators in Banach spaces

32%
Pietsch A.
Studia Mathematica
|
1974
|
tom 51
|
nr 3
201-223
10
Content available remote

Small ideals of operators

26%
Pietsch A.
Studia Mathematica
|
1974
|
tom 51
|
nr 3
265-267
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