Abstract
In this paper we study some parallelisms between ?-Aluthge transform and binormal operators on a Hilbert space via the Moore-Penrose inverse. Moreover, we give some applications of these results on the Lambert multiplication operators acting on L2(?).
Highlights
AND PRELIMINARIESLet B(H) denote the C∗-algebra of all bounded linear operators on a complex Hilbert space H
Recall that for T ∈ B(H), there is a unique factorization T = U |T |, where N (T ) = N (U ) = N (|T |), U is a partial isometry, i.e. U U ∗U = U, and |T | = (T ∗T )1/2 is a positive operator. This factorization is called the polar decomposition of T
If T = U |T | is the polar decomposition of T ∈ B(H), T = |T |1/2U |T |1/2 is called the Aluthge transformation of T
Summary
Let B(H) denote the C∗-algebra of all bounded linear operators on a complex Hilbert space H. Recall that for T ∈ B(H), there is a unique factorization T = U |T |, where N (T ) = N (U ) = N (|T |), U is a partial isometry, i.e. U U ∗U = U , and |T | = (T ∗T )1/2 is a positive operator. This factorization is called the polar decomposition of T. Let CR(H) be the set of all bounded linear operators on H with closed range.
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