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Traces and symmetric linear forms
The famous Calkin theorem says that there is a one-to-one correspondence between all ideals of operators on the separable infinite-dimensional...
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The Spectrum of Shift Operators and the Existence of Traces
This is a counterpart of the paper ‘Commutator structure of operator ideals’ written by Dykema, Figiel, Weiss, and Wodzicki. However, contrary to...
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A New Approach to Operator Ideals on Hilbert Space and Their Traces
In a series of papers, I developed a new approach to operator ideals on the infinite-dimensional separable Hilbert space and their traces. Step by...
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Traces on Operator Ideals and Related Linear Forms on Sequence Ideals (Part IV)
The concept of a dyadic representation was used for the first time in 1963, when I constructed traces of operators (acting on a Banach space) whose...
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Cantor–Bernstein theorems for certain symmetric bases in Banach spaces
We prove the following Cantor–Bernstein type theorem, which applies well to the class of symmetric sequence spaces studied earlier by Altshuler,...
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Traces and Residues of Pseudo-Differential Operators on the Torus
This paper is the outcome of an attempt to understand the connection between singular traces and the Wodzicki residues of pseudo-differential...
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On the Hadamard Sequence Spaces h p (X) and the p-Summing Operators
We consider the p -HH-norms and the Hadamard sequence space h p ( X ), where X is a normed space. We discuss the dual space of h p ( X ). We consider a...
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Connes–Dixmier Versus Dixmier Traces
This paper is a continuation of Pietsch (Math. Nachr. 285, 1999–2028,
2012 ) and (Stud. Math. 214, 37–66,2013 ). Now we are able to bring in the... -
Convergence and left-K-sequential completeness in asymmetrically normed lattices
If ( X ,∥.∥) is a real normed lattice, then p ( x )=∥ x + ∥ defines an asymmetric norm on X . We study the convergence of sequences in the asymmetrically...
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The 2-concavification of a Banach lattice equals the diagonal of the Fremlin tensor square
We investigate the relationship between the diagonal of the Fremlin projective tensor product of a Banach lattice E with itself and the...
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On spaces admitting no ℓ p or c 0 spreading model
It is shown that for each separable Banach space X not admitting ℓ 1 as a spreading model there is a space Y having X as a quotient and not admitting...
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Some topological and geometric properties of generalized Euler sequence space
In this paper, we introduce the Euler sequence space e r ( p ) of nonabsolute type and prove that the spaces e r ( p ) and l ( p ) are linearly isomorphic....
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On Orlicz-Power Series Spaces
In this manuscript, we investigate the isomorphisms of Orlicz-Köthe sequence spaces and quasidiagonal isomorphisms of Cartesian products of...
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A Characterization of Schauder Frames Which Are Near-Schauder Bases
A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which...
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On Operator-valued Measurable Functions
In this paper we discuss several results about classes of vector-valued (more specifically, operator-valued) measurable functions. The results we...
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Soft Ideals and Arithmetic Mean Ideals
This article investigates the soft-interior (se) and the soft-cover (sc) of operator ideals. These operations, and especially the first one, have...