Results 21 to 30 of about 76,262 (55)
arXiv, 2018 Let $ x=(x_{n})_{n} $ be a bounded complex sequence and let $M_{x} = \sup_n |x_n|$. By using a normaloid operator related to the sequence $ x=(x_{n})_{n} $, we prove that $$ \sup_{\lambda \in \mathbb{C}, |\lambda| \leq M_x} \sup_n |x_n+\lambda| = 2M_x.$$
arxiv
Multipliers on Noncommutative Orlicz Spaces [PDF]
, 2012 We establish very general criteria for the existence of multiplication operators between noncommutative Orlicz spaces $L^{\psi_0}(\tM)$ and $L^{\psi_1}(\tM)$. We then show that these criteria contain existing results, before going on to briefly look at the extent to which the theory of multipliers on Orlicz spaces differs from that of $L^p$-spaces.
arxiv +1 more source
Some generalized numerical radius inequalities for Hilbert space operators [PDF]
Sattari, Mostafa; Moslehian, Mohammad Sal; Yamazaki, Takeaki. Some
generalized numerical radius inequalities for Hilbert space operators. Linear
Algebra Appl. 470 (2015), 216--227, 2014 We generalize several inequalities involving powers of the numerical radius for product of two operators acting on a Hilbert space. For any $A, B, X\in \mathbb{B}(\mathscr{H})$ such that $A,B$ are positive, we establish some numerical radius inequalities for $A^\alpha XB^\alpha$ and $A^\alpha X B^{1-\alpha}\,\,(0 \leq \alpha \leq 1)$ and Heinz means ...
arxiv
Anticommutator Norm Formula for Projection Operators [PDF]
arXiv, 2016 We prove that for any two projection operators $f,g$ on Hilbert space, their anticommutator norm is given by the formula \[\|fg + gf\| = \|fg\| + \|fg\|^2.\] The result demonstrates an interesting contrast between the commutator and anticommutator of two projection operators on Hilbert space.
arxiv
Parallelism in Hilbert $K(\mathcal{H})$-modules [PDF]
arXiv, 2018 Let $(\mathcal{H}, [\cdot, \cdot ])$ be a Hilbert space and $K(\mathcal{H})$ be the $C^*$-algebra of compact operators on $\mathcal{H}$. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert $K(\mathcal{H})$-module $\mathcal{E}$ by employing the minimal projections on $\mathcal{H}$.
arxiv
The operator--valued parallelism and norm-parallelism in matrices [PDF]
arXiv, 2018 Let $\mathcal{H}$ be a Hilbert space, and let $K(\mathcal{H})$ be the $C^*$-algebra of compact operators on $\mathcal{H}$. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert $K(\mathcal{H})$-module by employing the Birkhoff--James orthogonality.
arxiv
Derivations on triangular Banach algebras of order three [PDF]
arXiv, 2013 In this paper, we define some new notions of triangular Banach algebras and we investigate the derivations on these algebras.
arxiv
Some estimates for the norm of the self-commutator [PDF]
arXiv, 2014 Different estimates for the norm of the self-commutator of a Hilbert space operator are proposed. Particularly, this norm is bounded from above by twice of the area of the numerical range of the operator. An isoperimetric-type inequality is proved.
arxiv
Operator versions of Hölder inequality and Hilbert $C^*$-modules [PDF]
arXiv, 2019 Recently proved weighted Cauchy Scwarz inequality for Hilbert $C^*$-modules leads to many H\"older type inequalities for unitarily invariant norms on Hilbert space operators.
arxiv
A Note Around Operator Bellman Inequality [PDF]
arXiv, 2019 In this paper, we shall give an extension of operator Bellman inequality. This result is estimated via Kantorovich constant.
arxiv