Advances in Operator Theory and Inequalities

This study examines the lower and upper bounds of the numerical radius and the Crawford number functions of bounded linear operators on Banach spaces. It also explores some convergence properties of these functions for sequences of uniformly converging Banach space operators. Later on, similar problems are addressed in the case of sectorial operators.

Keywords: Numerical radius, Crawford...

Let $\mathcal{H}$ be a complex Hilbert space, and let $\mathcal{B}(\mathcal{H})$ denote the algebra of all bounded linear operators on $\mathcal{H}$. For every $T\in \mathcal{B}(\mathcal{H})$, we denote by $T^{\ast}$ the adjoint of $T$. An operator $T\in \mathcal{B}(\mathcal{H})$ is said to be m-symmetric if
$$\sum_{k=0}^m (-1)^{k}\left(\begin{array}{l}
m \
k
\end{array}\right)T^{\ast...

The mixed Cauchy-Schwarz inequality is improved to prove several Berezin radius inequalities. Berezin radius inequalities are obtained by using the doubly convex function. Furuta's inequality and with a generalization of mixed Cauchy-Schwarz inequality, demonstrates Berezin radius inequalities.

Identifying the isometries on a normed linear space is one of the fundamental goals in functional analysis and operator theory. The classical Blanco–Koldobsky–Turn\v{s}ek theorem characterizes the isometries as the norm-one linear operators that preserve Birkhoff–James orthogonality. In this study, we consider the local preservation of Birkhoff–James orthogonality by linear operators between...

Our aim in this work is to give new inequalities of the d-tuples
of operators on a complex Hilbert space. An extension of the generalized some inequalities are proved for multivarible operators on a complex Hilbert space. Based on that some numerical radius inequalities due for a single operator.

In this talk, we give an overview of the power inequality for the numerical radius, which has been known for so long. Then, we present a some new progress related to this important inequality.

Inspired by state space theory in $C^*$-algebras, we study state spaces in Banach spaces--the family of norm-one support functionals for the unit ball at a given unit vector. This generalizes the state space of a unital $C^*$-algebra because it is the family of norm-one support functionals for the unit ball at the multiplicative unit. The state space of $X$ associated with a unit vector $x\in...

Abstract:
This paper reviews some of the results obtained by the authors in their recent work on matrix inequalities involving sectorial matrices and a matrix monotone function defined by the harmonic mean integral. The study focuses on the important concept of matrix inequalities that relate to the Schur complement of sectorial matrices with respect to a matrix monotone function.
if $A$ and...

FURTHER GENERALIZED NUMERICAL RADIUS
INEQUALITIES FOR HILBERT SPACE OPERATORS

Vuk Stojiljković

$^1$ Mathematical Institute of Serbian Academy of Sciences and Arts,
Kneza Mihaila 36, Belgrade 11000, Serbia
[email protected]

We introduce a new generalized numerical radius, $w_{h,g}^{Re}(A)$, which is defined based on the generalized real and...

By a systematic development of fundamental concepts of conformable calculus we establish conformable divergence theorem and Green's identities which we combine with some new anisotropic Picone-type identities to derive a generalized anisotropic Hardy type inequality with weights and conformable fractional differential operators. As a consequence, several Hardy type inequalities and Heisenberg...

Representations induced by general positive sesquilinear maps with values in ordered Banach bimodules such as commutative and non-commutative
L1-spaces and the spaces of bounded linear operators from a
C-algebra into the dual of another C-algebra are considered. As a starting point, a generalized Cauchy-Schwarz inequality is proved for these maps and a representation of bounded positive...

In this talk, we provide a complete characterization of the convexity of the Berezin range of composition operators on weighted Bergman spaces. Moreover, we show that while the origin lies in the closure of the Berezin range, it does not belong to the range itself.

The quantum ground operator underlies every action of a field and that preserves the energy state of a system, maintaining the law of conservation of energy of the dynamical system given by its corresponding Lagrangian.and giving it a direction in space-time. Said operator will be a fundamental part in the system transformations in field theory and to define the field intentionality. In a...

In this article, we study Bohr-type inequalities involving a parameter or convex combinations for $K$-quasiconformal, sense-preserving harmonic mappings in $\mathbb{D}$, where the analytic part is subordinate to a convex function. Moreover, we establish similar inequalities when the subordinating function is chosen from the class of concave univalent functions with pole $p$, as well as from...

abstract
Berezin numbers and their generalizations play a significant role in operator theory, particularly in the study of inequalities in Hilbert spaces. They also find applications in functional analysis, non-commutative geometry, and quantum physics. In this paper, we investigate several improvements and extensions of Berezin-type inequalities for bounded linear operators. We introduce...

In this paper, we give several p-numerical radius inequalities for
products of Hilbert space operators. For the particular case, we reobtain some earlier existing bounds. Also, we provide new inequalities for the classical numerical radius.