Fuglede-putnam theorem for (p, k)-quasihyponormal and class (Y )operators
AuthorBakir, Aissa Nasli
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CitationBakir, A. N. (2009). Fuglede-putnam theorem for (p, k)-quasihyponormal and class (Y )operators. Maltepe Üniversitesi. s. 76.
Let A and B be normal operators on a complex separable Hilbert space H. The equation AX = XB implies A ∗X = XB∗ for some operatorX on H ino itself is known as the familiar Fuglede-Putnam theorem. An operator A ∈ B(H) is said to be log-hyponormal if A is invertible and log(A ∗A) ≥ log(AA∗ ), class (Y ) if there exist α ≥ 1 and kα > 0 such that |AA∗ − A ∗A| α ≤ k 2 α (A − λ) ∗ (A − λ) for all λ ∈ C, dominant if ran(A − λ) ⊆ ran(A − λ) ∗ for all λ ∈ σ(A) where σ(A) denotes the spectrum ofA. A is called (p, k)-quasihyponormal if A ∗k ((A ∗A) p − (AA∗ ) p )A k ≥ 0, k ∈ N, 0 < p ≤ 1. In this talk, we’ll give an extension of Fuglede-Putnam’s result to the case when either 1) A is log-hyponormal operator and B ∗ is a class (Y ) operator 2) A is (p, k)-quasihyponormal operator with ker A ⊆ ker A ∗ and B ∗ is dominant. Other results are also given.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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