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Abstract.In this paper, we shall give an operator transform
$${\hat T}$$ from class A to the class of hyponormal operators. Then we shall show that
$$\sigma (T) = \sigma (\hat T)$$ and
$$\sigma_a (T)… (More)

Abstract For “criss-cross commuting” tuples A and B of Banach space operators we give two sufficient conditions for the spectral equality σ T ( AB )= σ T ( BA ).

For an operator T with some trace class condition, let gT n and g P T n be the principal functions related to the Cartesian decomposition T n = Xn + iYn and the polar decomposition T n = Un|T n | for… (More)

Bonsall and Duncan's book ([1, Theorem 25.6]) exhibits a normal element h + ik of a Banach algebra such that r(h + ik) 1980 Mathemnatics Subject Classification (1985 Revision). Primary 47A12;… (More)

Let U be the unilateral shift on l2. For any complex numbers α and β, put T = αU + βU* and S = T 2. Then we show that the operator S is convexoid.