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Generalized multivalued contractions which are quasi-bounded

Petrusel G.

Demonstratio Mathematica

2007

Vol. 40, nr 3

639-648

The purpose of this note is to study the following problem: which multi- valued generalized contractions are quasi-bounded with the quasi-norm strictly less than 1 ? As consequences, some surjectivity results are given.

On summing and related operators acting from a Hilbert space

Tien N., Tarieladze V., Vidal R.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 4

365-375

We study the situation when the behaviour of an operator from a Hilbert space to a Banach space on all orthonormal bases determines whether it belongs to a prescribed class of operators. The cases of (q, 2)-summing, almost summing and [gamma]-summing operators are treated in a unified way.