FACTORIZATION OF k-QUASIHYPONORMAL OPERATORS

Let A be the class of all operators T on a Hilbert space H such that R(T*^kT), the range space of T*^kT, is contained in R(T*^(k+1)), for a positive integer k. It has been shown that if T ε A, there exists a unique operator C_T on H such that(i) T*^kT=T*^(k+1)C_T; (ii)‖C_T‖^2=inf{μ: μ ≥ 0 and (T*^kT)(T*^kT)*≤μ T*^(k+1) T*^(k+1)}; (iii) N(C_T)=N(T*^kT) and (iv) R(C_T) ⊆ R(T^(k+1)) The main objective of this paper is to characterize k-quasihyponormal; normal, and self-adjoint operators T in A in terms of C_T. Throughout the paper, unless stated otherwise, H will denote a complex Hilbert space and T an operator on H, i.e., a bounded linear transformation from H into H itself. For an operator T, we write R(T)and N(T) to denote the range space and the null space of T.

並列關鍵字

Self-adjoint ； normal ； unitary ； quasinormal ； hyponormal ； quasihyponormal ； k-quasihyponormal ； isometry ； partial isometry ； null space ； range space and the projection

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