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Quasicompact endomorphisms of commutative semiprime Banach algebras

Joel F. Feinstein, Herbert Kamowitz (2010)

Banach Center Publications

This paper is a continuation of our study of compact, power compact, Riesz, and quasicompact endomorphisms of commutative Banach algebras. Previously it has been shown that if B is a unital commutative semisimple Banach algebra with connected character space, and T is a unital endomorphism of B, then T is quasicompact if and only if the operators Tⁿ converge in operator norm to a rank-one unital endomorphism of B. In this note the discussion is extended in two ways: we discuss endomorphisms of commutative...

Quasi-invariant subspaces generated by polynomials with nonzero leading terms

Kunyu Guo, Shengzhao Hou (2004)

Studia Mathematica

We introduce a partial order relation in the Fock space. Applying it we show that for the quasi-invariant subspace [p] generated by a polynomial p with nonzero leading term, a quasi-invariant subspace M is similar to [p] if and only if there exists a polynomial q with the same leading term as p such that M = [q].

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