On extensions of some Flugede–Putnam type theorems involving (p,k)‐quasihyponormal,spectral, and dominant operators |
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| Authors: | Kotaro Tanahashi S M Patel Atsushi Uchiyama |
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| Institution: | 1. Department of Mathematics, Tohoku Pharmaceutical University, Sendai 981‐8558, Japan;2. Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, Gujarat, India;3. Department of Mathematical Sciences, Faculty of Science, Yamagata University, Yamagata 990‐8560, Japan |
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| Abstract: | A Hilbert space operator S is called (p, k)‐quasihyponormal if S *k ((S *S)p – (SS *)p )Sk ≥ 0 for an integer k ≥ 1 and 0 < p ≤ 1. In the present note, we consider (p, k)‐quasihyponormal operator S ∈ B (H) such that SX = XT for some X ∈ B (K,H) and prove the Fuglede–Putnam type theorems when the adjoint of T ∈ B (K) is either (p, k)‐quasihyponormal or dominant or a spectral operator (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Fuglede− Putnam theorem (p k)‐quasihyponormal operator dominant operator |
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