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k-Quasihyponormal operators are subscalar
Authors:Eungil Ko
Affiliation:1. Department of Mathematics, Ewha Women's University, 120-750, Seoul, Korea
Abstract:In this paper we shall prove that if an operatorTL(⊕ 1 2 H) is an operator matrix of the form $$T = left( {begin{array}{*{20}c} {T_1 } & {T_2 } 0 & {T_3 } end{array} } right)$$ whereT 1 is hyponormal andT 3 k =0, thenT is subscalar of order 2(k+1). Hence non-trivial invariant subspaces are known to exist if the spectrum ofT has interior in the plane as a result of a theorem of Eschmeier and Prunaru (see [EP]). As a corollary we get that anyk-quasihyponormal operators are subscalar.
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