Abstract
We study subspaces of algebraL(X) which are invariant with respect to all similarity transformations and give a full description of these subspaces for finite-dimensional spaceX, for separable Hilbert spaceX and forX=l p (1≤p<∞) orc 0. The problem is equivalent to a study of Lie ideals inL(X).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Apostol,Commutators on l p-spaces, Rev. Roum. Math. Pures et Appl.17 (1972), 1513–1534.
A. Brown, C. Pearcy,Structure of commutators of operators, Ann. of Math.82 (1965), 112–127.
J. W. Calkin,Two sides ideals and congruences in the ring of bounded operators in Hilbert space, Ann. of Math.42 (1941), 839–873.
I. Glazman, Yu. Lyubich,Finite-dimensional linear analysis, MIT Press, Cambridge and London, 1974.
I. Gohberg, A. Markus, I. Feldman,Normally solvable operators and ideals associated with them, Amer. Math. Soc. Transl. (2)61 (1967), 63–84.
W. T. Gowers, B. Maurey,Banach spaces with small spaces of operators, Math. Ann.307 (1997), 543–568.
M. I. Kadec, M. G. Snobar,Certain functionals on the Minkowski compactum, Math. Notes10 (1971), 694–696.
A. Markus, A. Semencul,Operators that weakly perturb the spectrum, Siberian Math. J.19 (1978), 455–460.
B. Mityagin,The homotopy structure of the linear group of a Banach space, Russian Math. Surveys25, N 5 (1970), 59–103.
A. Pietsch,Operator ideals, North-Holland, Amsterdam-New York-Oxford, 1980.
W. Rudin,Functional analysis, McGraw-Hill, 1973.
C. Schneeberger,Commutators on a separable L p-space, Proc. Amer. Math. Soc.28 (1971), 464–472.
Author information
Authors and Affiliations
Additional information
Partially supported by Israel Science Foundation, Grant 216/98.