×

On generalized volume ratio numbers. (English) Zbl 0771.46010

Summary: We define volume ratio numbers of operators between arbitrary Banach spaces and prove results about fundamental properties such as duality and eigenvalue estimates. Several connections to \(K\)-convexity, other \(s\)- numbers and to the theory of weak type and weak cotype also arise.

MSC:

46B20 Geometry and structure of normed linear spaces
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
PDF BibTeX XML Cite