Titlebook: Geometric Aspects of Functional Analysis; Israel Seminar (GAFA J. Lindenstrauss,V. Milman Conference proceedings 1995 Birkh?user Verlag 199

Ardent

胰臟

https://doi.org/10.1007/978-1-4612-2140-1Let . = (..) be positive definite Hermitian . × . matrix. We prove a following strengthening of the Hadamard inequality:.We give similar estimate in the case of non-Hermitian matrix. We use these results for a short proof of the existence of Von Koh’s infinite determinants, and also give a strong isoperimetric inequality for simplices in ?.

憂傷

蛤肉

一再煩擾

緊張過度

,Remarks on Bourgain’s Problem on Slicing of Convex Bodies,For a convex symmetric body . ? ?. we define a number .. by:. If the minimum is attained for . = . we say that . is in isotropic position. Any K has an affine image which is in isotropic position.

GREG

A Note on the Banach-Mazur Distance to the Cube,If . is an .-dimensional normed space, and . denotes the Banach-Mazur distance, then .(., ?.) ≤ ...

gentle

Uniform Non-Equivalence between Euclidean and Hyperbolic Spaces,It is well known that the Euclidean and hyperbolic (Lobachevsky-Bolyai) spaces .., .. of the same dimension . are homeomorphic. V. A. Efremovich ([1], [2]) proved in 1945, that .. and .. are not uniformly homeomorphic; this means that there does not exist any homeomorphism between them that is uniform together with its inverse.

貪婪性

A Remark about Distortion,In this note we show that every Banach space . not containing .. uniformly and with unconditional basis contains an arbitrarily distortable subspace.

Conjuction

Symmetric Distortion in ,,,We take notation and definitions from the preceding Note [M].