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

ACME

,On the Richness of the Set of ,’s in Krivine’s Theorem,We give examples of two Banach spaces. One Banach space has no spreading model which contains .. (1 ≤ . < ∞) or ... The other space has an unconditional basis for which .. (1 ≥ . < ∞) and .. are block finitely represented in all block bases.

牢騷

嚴(yán)厲譴責(zé)

Determinant Inequalities with Applications to Isoperimatrical Inequalities,Let . = (..) 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 ?.

說笑

considerable

不透氣

Projection Functions on Higher Rank Grassmannians,ow that the behaviour in the case of higher rank manifolds is often very different from the rank 1 case. We also study the images of projection functions under Radon transforms. If X is an .-dimensional normed space, and . denotes the Banach-Mazur distance, then .(., ..) ≤ ...

Foregery

On the Volume of Unions and Intersections of Balls in Euclidean Space,. – ..| for all ., ., does it follow that. where |. | is the Euclidean norm and B(.) is the ball centered at . and of radius .? Under some additional assumptions, we give a probabilistic proof of this and of other related results.

閑逛

NOTCH

Proportional Subspaces of Spaces with Unconditional Basis Have Good Volume Properties,here exist ..,…, .. ? . such that .. ? .{..…, ..} and. This answers a question of V. Milman which appeared during a GAFA seminar talk about the hyperplane problem. We add logarithmical estimates concerning the hyperplane conjecture for proportional subspaces and quotients of Banach spaces with uncon

insert

Asymptotic Infinite-Dimensional Theory of Banach Spaces,e 50s and 60s; goals of the theory had direct roots in and were natural expansion of problems from the times of Banach. Most of surveys and books of that period directly or indirectly discussed such problems as the existence of unconditional basic sequences, the c.-..-reflexive subspace problem and