## 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