Let H and K be complex Hilbert spaces, let L(H,K) be the set of bounded linear operators from H to K and write L(H) := L(H,H). An operator T ∈ L(H) is said to be normal if T ∗T = TT ∗, hyponormal if T ∗T ≥ TT ∗, and subnormal if T = N |H, where N is normal on some Hilbert space K ⊇ H. If T is subnormal then T is also hyponormal. Recall that the Hilbert space L2(T) has a canonical orthonormal ba...

Weyl’s theorem for an operator says that the complement in the spectrum of the Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. H. Weyl ([22]) discovered that this property holds for hermitian operators and it has been extended from hermitian operators to hyponormal operators and to Toeplitz operators by L. Coburn ([5]), and to sever...

In this paper, we prove some basic results for Cauchy dual of weighted composition operators. Also introduce new classes operators, called ?-hyponormal, ?-quasi-hyponormal, and provide necessary sufficient conditions MP-inverse operators on L2(?) to belong these classes. addition, study the complex symmetry types Moreover, examples are provided illustrate obtained results.

Let L(H) denote the C∗-algebra of adjointable operators on a Hilbert C∗-module H. In this paper, we introduce generalized Cauchy–Schwarz inequality for in L(H). More precisely, an operator A∈L(H) is said to satisfy if there exists ν∈(0,1) such that ‖⟨Ax,y⟩‖≤(‖Ax‖‖y‖)ν(‖Ay‖‖x‖)1−ν(x,y∈H).We investigate various properties which inequality. particular, prove A satisfies has polar decomposition, th...

The intertwining relations between cosubnormal and closed hyponormal (resp. cohyponormal and closed subnormal) operators are studied. In particular, an asymmetric Putnam–Fuglede theorem for unbounded operators is proved.

The aim of this paper was to introduce and investigate a new seminorm operator tuples on complex Hilbert space H when an additional semi-inner product structure defined by positive (semi-definite) A is considered. We prove the equality between well-known A-joint in case A-doubly-commuting A-hyponormal operators. This study extension result [Results Math 75, 93(2020)] allows us show that followi...

We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem, and we obtain new necessary and sufficient conditions to guarantee that the spectral mapping theorem holds for the B-Weyl spectrum and for polynomials in T. We also prove that the spectral mapping theorem holds for the B-Browder spectrum and for analytic functions on an open n...