354 research outputs found
Spectral conditions on Lie and Jordan algebras of compact operators
We investigate the properties of bounded operators which satisfy a certain
spectral additivity condition, and use our results to study Lie and Jordan
algebras of compact operators. We prove that these algebras have nontrivial
invariant subspaces when their elements have sublinear or submultiplicative
spectrum, and when they satisfy simple trace conditions. In certain cases we
show that these conditions imply that the algebra is (simultaneously)
triangularizable.Comment: 14 page
Matrix Algebras with a Certain Compression Property I
An algebra of complex matrices is said to be
projection compressible if is an algebra for all orthogonal
projections . Analogously, is said
to be idempotent compressible if is an algebra for all
idempotents . In this paper we construct several
examples of unital algebras that admit these properties. In addition, a
complete classification of the unital idempotent compressible subalgebras of
is obtained up to similarity and transposition. It
is shown that in this setting, the two notions of compressibility agree: a
unital subalgebra of is projection compressible if
and only if it is idempotent compressible. Our findings are extended to
algebras of arbitrary size in the sequel to this paper.Comment: 23 page
Strict quantizations of almost Poisson manifolds
We show the existence of (non-Hermitian) strict quantization for every almost
Poisson manifold.Comment: 15 page
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