Generalized Nash-Moser smoothing operators and the structure of Fréchet spaces
Uniquely Generated Grothendieck Space Ideals.
On ideals of operators and of locally convex spaces.
On the Schatten S classes.
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.
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.
Singly generated ideals of locally convex spaces
On a Question of Pełczyński about Strictly Singular Operators
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 p-summable sequences in locally convex spaces.
Some problems for suggested thinking in Fréchet space theory.
On the -characteristic of fractional powers of linear operators
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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