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On the Schatten S classes.

Marilda A. Simôes — 1991

Extracta Mathematicae

The Schatten Sp classes, 1 ≤ p ≤ ∞, were introduced and studied in [6] in connection with the problem of finding suitable classes of operators having a well-defined trace. In this paper we consider a generalization Sφ of the Schatten classes Sp obtained in correspondence with opportune, continuous, strictly increasing, sub-additive functions φ: [0,∞) → [0,∞) such that φ(0) = 0 and φ(1) = 1. Our purpose is to study the spaces...

On the space of φ-nuclear operators on l.

Marilda A. Simoes — 1990

Collectanea Mathematica

We consider the generalization Sphi of the Schatten classes Sp obtained in correspondence with opportune continuous, strictly increasing, sub-additive functions phi such that phi(0) = 0 and phi(1) = 1. The purpose of this note is to study the spaces Sphi of the phi-nuclear operators and to compare their properties to those of the by now well-known space S1 of nuclear operators.

On a Question of Pełczyński about Strictly Singular Operators

Jesús M. F. CastilloMarilda SimoesJesús Suárez de la Fuente — 2012

Bulletin of the Polish Academy of Sciences. Mathematics

We exhibit new examples of weakly compact strictly singular operators with dual not strictly cosingular and characterize the weakly compact strictly singular surjections with strictly cosingular adjoint as those having strictly singular bitranspose. We then obtain new examples of super-strictly singular quotient maps and show that the strictly singular quotient maps in Kalton-Peck sequences are not super-strictly singular.

On the -characteristic of fractional powers of linear operators

Jürgen AppellMarilda A. SimõesPetr P. Zabrejko — 1994

Commentationes Mathematicae Universitatis Carolinae

We describe the geometric structure of the -characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss- Ovchinnikov interpolation theorems, as well as on the Krasnosel’skij-Krejn factorization theorem.

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