Filomat 2022 Volume 36, Issue 1, Pages: 289-301
https://doi.org/10.2298/FIL2201289Z
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The λ-Aluthge transform and its applications to some classes of operators
Zid Sohir (Laboratory of Mathematical Techniques (LTM), Department of Mathematics, Faculty of Mathematics and Informatics, University of Batna, Batna, Algeria), s.zid@univ-batna2.dz
Menkad Safa (Laboratory of Mathematical Techniques (LTM), Department of Mathematics, Faculty of Mathematics and Informatics, University of Batna, Batna, Algeria), s.menkad@univ-batna2.dz
Let T ∈ B(H) be a bounded linear operator on a Hilbert space H, and let T =
U|T| be its polar decomposition. Then, for every λ ∈ [0,1] the λ-Aluthge
transform of T is defined by Δλ(T) = |T|λU|T|1-λ. In this paper, we
characterize the invertible, binormal, and EP operators and its intersection
with a special class of introduced operators via the λ-Aluthge transform.
Keywords: Polar decomposition, binormal operators, closed range operators, λ-Aluthge transform, Moore-Penrose inverse
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