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Über schwach zyklische Abbildungen in nichtlinearen Produkträumen und einige Monotonieaussagen

Christian P. Ullrich (1979)

Aplikace matematiky

In der Arbeit werden einige Eigenschaften der sog. schwach zyklischen Vektorfunktionen untersucht. Die allgemeine Deffinition einer schwach zyklischen Funktion enthält als einen Spezialfall Funktionen der Form A x mit einer schwach zyklischen Matrix A . Es werden insbesondere Monotonie Eigenschaften schwach zyklischer Funktionen betrachtet, wobei die Monotonie in verallgemeinertem Sinn definiert wird.

U-ideals of factorable operators

Kamil John (1999)

Czechoslovak Mathematical Journal

We suggest a method of renorming of spaces of operators which are suitably approximable by sequences of operators from a given class. Further we generalize J. Johnsons’s construction of ideals of compact operators in the space of bounded operators and observe e.g. that under our renormings compact operators are u -ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space.

Ultraweakly compact operators and dual spaces

Teresa Alvarez (2004)

Bollettino dell'Unione Matematica Italiana

In this paper, the class of all bounded ultraweakly compact operators in Banach spaces is introduced and characterised in terms of their first and second conjugates. We analize the relationship between an ultraweakly compact operator and its conjugate. Examples of operators belonging to this class are exhibited. We also investigate the connection between ultraweak compactness of T L X , Y and minimal subspaces of Y and we present a result of factorisation for ultraweakly compact operators.

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