Related papers: Norms of basic operators in vector valued model sp…

Motivated by a question of Vincent Lafforgue, we study the Banach spaces $X$ satisfying the following property: there is a function $\vp\to \Delta_X(\vp)$ tending to zero with $\vp>0$ such that every operator $T\colon L_2\to L_2$ with…

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…

We present several operator and norm inequalities for Hilbert space operators. In particular, we prove that if $A_{1},A_{2},...,A_{n}\in {\mathbb B}({\mathscr H})$, then…

The objective of this paper is to find an estimation of the essential norm of Riemann-Stieltjes operator from the spaces $F(p,q,s)$ ( general function space) and $H(p,q,\phi)$ (mixed-norm space) into Zygmund-type space in the unit ball of…

We consider a family of norms (called operator E-norms) on the algebra $B(H)$ of all bounded operators on a separable Hilbert space $H$ induced by a positive densely defined operator $G$ on $H$. Each norm of this family produces the same…

We consider pairs of operators $A,B\in B(H)$, where $H$ is a Hilbert space, such that there exist a linear isometry $f$ from the span of $\{A,B\}$ into $\mathbb{C}^2$ mapping $A,B$ into orthonormal vectors. We prove some necessary…

We give an elementary symmetric function expansion for $M\Delta_{m_\gamma e_1}\Pi e_\lambda^{\ast}$ and $M\Delta_{m_\gamma e_1}\Pi s_\lambda^{\ast}$ when $t=1$ in terms of what we call $\gamma$-parking functions and lattice $\gamma$-parking…

For an $N \times T$ random matrix $X(\beta)$ with weakly dependent uniformly sub-Gaussian entries $x_{it}(\beta)$ that may depend on a possibly infinite-dimensional parameter $\beta\in \mathbf{B}$, we obtain a uniform bound on its operator…

In this paper, we discuss hyponormal block Toeplitz operators $T_{\Phi}$ over the vector-valued weighted Bergman space $A_\alpha^2\left(\mathbb{C}^n\right)$. And two conditions about hyponormal block Toeplitz operators $T_{\Phi}$ on…

The main purpose of this paper is to study the generalized Hilbert operator {equation*} \mathcal{H}_g(f)(z)=\int_0^1f(t)g'(tz)\,dt {equation*} acting on the weighted Bergman space $A^p_\om$, where the weight function $\om$ belongs to the…

In this paper, we aim to introduce and characterize the concept of numerical radius orthogonality of operators on a complex Hilbert space $\mathcal{H}$ which are bounded with respect to the semi-norm induced by a positive operator $A$ on…

We study a family of non-C2-cofinite vertex operator algebras, called the singlet vertex operator algebras, and connect several important concepts in the theory of vertex operator algebras, quantum modular forms, and modular tensor…

Several refinements of norm and numerical radius inequalities of bounded linear operators on a complex Hilbert space are given. In particular, we show that if $A$ is a bounded linear operator on a complex Hilbert space, then $$…

Let $T$ be a weakly almost periodic (WAP) linear operator on a Banach space $X$. A sequence of scalars $(a_n)_{n\ge 1}$ {\it modulates} $T$ on $Y \subset X$ if $\frac1n\sum_{k=1}^n a_kT^k x$ converges in norm for every $x \in Y$. We obtain…

In this note we address various algorithmic problems that arise in the computation of the operator norm in unitary representations of a group on Hilbert space. We show that the operator norm in the universal unitary representation is…

We study the space of vector valued theta functions for the Weil representation of a positive definite even lattice of rank two with fundamental discriminant. We work out the relation of this space to the corresponding scalar valued theta…

Let $A$ be a positive definite operator on a Hilbert space $H$, and $|||.|||$ be a unitarily invariant norm on $B(H)$. We show that if $f$ is an operator monotone function on $(0,\infty)$ and $n\in \mathbb{N}$, then $|||D^n…

Every four-dimensional ${\cal N}=2$ superconformal field theory comes equipped with an intricate algebraic invariant, the associated vertex operator algebra. The relationships between this invariant and more conventional protected…

In this work, firstly in the direct sum of Hilbert spaces of vector-functions $L^{2} (H,(-\infty,a_{1})) \oplus L^{2} (H,(a_{2},b_{2}))\oplus^{2} (H,(a_{3},+\infty))$, $- \infty<a_{1}<a_{2}<b_{2}<a_{3}<+\infty$ all normal extensions of the…

We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on the Hartogs triangle. The estimates of the…