Uniform factorization for p-compact sets of p-compact linear operators

Compact Sets and Compact Operators

Proof. Properties 2 and 3 are left to the reader. For property 1, assume that S is an unbounded compact set. Since S is unbounded, we may select a sequence {vn}n=1 such that ‖vn‖ → 0 as n→∞. Since S is compact, this sequence will have a convergent subsequence, say {vk}k=1, which will still be unbounded. This sequence is Cauchy, so there is a positive integer K for which ‖v`− vm‖ ≤ 1/2 for all `...

M-ideals of Compact Operators Intò P

We show for 2 p < 1 and subspaces X of quotients of L p with a 1-unconditional nite-dimensional Schauder decomposition that K (X; ` p) is an M-ideal in L(X; ` p).

P-Amenable Locally Compact Hypergroups

p-amenable locally compact hypergroups

0

DETERMINISTIC p-COMPACT GROUPS

We investigate the class of N -determined p-compact groups and the class of p-compact groups with N -determined automorphisms. A p-compact group is said to be N -determined if it is determined up to isomorphism by the normalizer of a maximal torus. The automorphisms of a p-compact group are said to be N -determined if they are determined by their restrictions to this maximal torus normalizer.