Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators
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Pintu Bhunia
Abstract
Let 𝓗 be a complex Hilbert space and A be a non-zero positive bounded linear operator on 𝓗. The main aim of this paper is to discuss a general method to develop A-operator seminorm and A-numerical radius inequalities of semi-Hilbertian space operators using the existing corresponding inequalities of bounded linear operators on 𝓗. Among many other inequalities we prove that if S, T, X ∈ 𝓑A(𝓗), i.e., if A-adjoint of S, T, X exist, then
Further, we prove that if T ∈ 𝓑A(𝓗), then
Here wA(⋅), cA(⋅) and ∥⋅∥A denote A-numerical radius, A-Crawford number and A-operator seminorm, respectively.
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( Communicated by Michal Zajac )
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Artikel in diesem Heft
- Regular Papers
- Variants of Booleanness: Congruences of a partial frame versus those of its free frame
- Models, coproducts and exchangeability: Notes on states on Baire functions
- Inverse tangent series involving pell and pell-lucas polynomials
- A new family of two-variable polynomials based on hermite polynomials
- Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function
- On the solvability of a fourth-order differential evolution equation on singular cylindrical domain in R4
- Investigation of an implicit Hadamard fractional differential equation with Riemann-Stieltjes integral boundary condition
- Stability criteria for systems of two first-order linear ordinary differential equations
- A perturbed eigenvalue problem in exterior domain
- On extensions of bilinear maps
- Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators
- Weighted composition operators from the Besov space into nth weighted type spaces
- Fuzzy ideal topological vector spaces
- Partial actions on convergence spaces
- On quasi-small loop groups
- Topologies generated by symmetric porosity on normed spaces
- The Alpha Power Rayleigh-G family of distributions
- An alternative for Laplace Birnbaum-Saunders distribution
- Existence of positive solutions for boundary value problems with p-Laplacian operator
