Related papers: On Some Numerical Radius Inequalities for Hilbert …
Let $A$ be a bounded linear operator defined on a complex Hilbert space and let $|A|=(A^*A)^{1/2}$ be the positive square root of $A$. Among other refinements of the well known numerical radius inequality $w^2(A)\leq \frac12 \|A^*A+AA^*\|$,…
We develop upper and lower bounds for the numerical radius of $2\times 2$ off-diagonal operator matrices, which generalize and improve on the existing ones. We also show that if $A$ is a bounded linear operator on a complex Hilbert space…
This paper investigates new properties of $q$-numerical ranges for compact normal operators and establishes refined upper bounds for the $q$-numerical radius of Hilbert space operators. We first prove that for a compact normal operator $T$…
In this paper, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequalities. In particular, we present \begin{align*}…
In this paper, we study the relationship between operator space norm and operator space numerical radius on the matrix space $\mathcal{M}_n(X)$, when $X$ is a numerical radius operator space. Moreover, we establish several inequalities for…
Let $A$ be an unbounded operator on a Banach space $X$. It is sometimes useful to improve the operator $A$ by extending it to an operator $B$ on a larger Banach space $Y$ with smaller spectrum. It would be preferable to do this with some…
This article has two interpenetrating motifs. One is an exposition of some major ideas and techniques behind the use of block matrices, and especially their positivity properties. This is done by focussing on one major problem:…
We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators related to the matrix order and the Jensen inequality.…
By the use of the celebrated Kato's inequality we obtain in this paper some new inequalities for trace class operators on a complex Hilbert space H. Natural applications for functions defined by power series of normal operators are given as…
We study different operator radii of homomorphisms from an operator algebra into $B(H)$ and show that these can be computed explicitly in terms of the usual norm. As an application, we show that if $\Omega$ is a $K$-spectral set for a…
Let $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$ be a complex Hilbert space and $A$ be a positive (semidefinite) bounded linear operator on $\mathcal{H}$. The semi-inner product induced by $A$ is given by ${\langle x\mid…
Let $\mathbb{A}= \begin{pmatrix} A & 0 \\ 0 & A \\ \end{pmatrix} $ be a $2\times2$ diagonal operator matrix whose each diagonal entry is a bounded positive (semidefinite) linear operator $A$ acting on a complex Hilbert space $\mathcal{H}$.…
We describe a new operator space structure on $L_p$ when $p$ is an even integer and compare it with the one introduced in our previous work using complex interpolation. For the new structure, the Khintchine inequalities and Burkholder's…
In this work, the mixed Schwarz inequality for semi-Hilbertian space operators is proved. Namely, for every positive Hilbert space operator $A$. If $f$ and $g$ are nonnegative continuous functions on $\left[0,\infty\right)$ satisfying…
Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity…
We prove numerical radius inequalities involving commutators of $G_{1}$ operators and certain analytic functions. Among other inequalities, it is shown that if $A$ and $X$ are bounded linear operators on a complex Hilbert space, then…
We study triplets of Hilbert space operators satisfying a certain inequality. A range inclusion theorem with norm estimate for those triplets is given with the language of Kre\u{\i}n space geometry and de Branges-Rovnyak space theory.
Relatively recently, K.M.R. Audenaert (2010), R.A. Horn and F. Zhang (2010), Z. Huang (2011), A.R. Schep (2011), A. Peperko (2012), D. Chen and Y. Zhang (2015) have proved inequalities on the spectral radius and the operator norm of…
This paper explores refinements of some operator norm inequalities through the generalized spherical Aluthge transform and the spherical Heinz transform. We introduce the spherical Schatten $p$-norm for operator tuples and establish several…
In this paper, we aim to introduce the notion of the spectral radius of bounded linear operators acting on a complex Hilbert space $\mathcal{H}$, which are bounded with respect to the seminorm induced by a positive operator $A$ on…