Premium
K ‐Theory for Algebras of Operators on Banach Spaces
Author(s) -
Laustsen Niels Jakob
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007206
Subject(s) - mathematics , banach space , ideal (ethics) , pure mathematics , operator theory , approximation property , space (punctuation) , discrete mathematics , computer science , philosophy , epistemology , operating system
It is proved that, for each pair ( m , n ) of non‐negative integers, there is a Banach space X for which K 0 ( B (X))≅Z m and K 1 ( B (X))≅Z n . The K ‐groups of all closed ideals of operators contained in the ideal of strictly singular operators are computed, and some results about the existence of splittings of certain short exact sequences are derived.