Related papers: Integral $K$-Operator Frames for $End_{\mathcal{A}…
In this paper, we introduce the concept of $K$-fusion frames and propose the duality for such frames. The relation between the local frames of $K$-fusion frames with their dual is studied. The elements from the range of a bounded linear…
Rigged modules over an operator algebra are a generalization of Hilbert modules over a $C^{\star}$-algebra. We characterize the rigged modules over an operator algebra $\mathcal A$ which are orthogonally complemented in $C_\infty(\mathcal…
In this paper, we investigate the spectrum of the self adjoint differential operator with operator coefficitent in a separable Hilbert space. We also derive asymptotic formulas for the sum of eigenvalues of this operator.
This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…
In this paper we study the small-$\lambda$ spectral asymptotics of an integral operator $\mathscr{K}$ defined on two multi-intervals $J$ and $E$, when the multi-intervals touch each other (but their interiors are disjoint). The operator…
In this paper, we will introduce the new concepts of continuous bi-g-frames and continuous K-bi-g-frame for Hilbert spaces. Then, we examine some characterizations properties with the help of a biframe operator. Finally, we investigate…
We consider the extension of the Heisenberg vertex operator algebra by all its irreducible modules. We give an elementary construction for the intertwining vertex operators and show that they satisfy a complex parametrized generalized…
Given a stationary continuous-time process $f(t)$, the Hilbert-Schmidt operator $A_{\tau}$ can be defined for every finite $\tau$\cite{Vautard1989SingularSA}. Let $\lambda_{\tau,i}$ be the eigenvalues of $A_{\tau}$ with descending order. In…
In this paper, we introduce the notion of invariant submodule in the theory of Hilbert C*-modules and study some basic properties of bounded adjointable operators and their generalized inverses which have nontrivial invariant submodules. We…
The methods of integral operators on the cohomology of Hilbert schemes of points on surfaces are developed. They are used to establish integral bases for the cohomology groups of Hilbert schemes of points on a class of surfaces (and…
We prove the existence of tight frames whose elements lie on an arbitrary ellipsoidal surface within a real or complex separable Hilbert space H, and we analyze the set of attainable frame bounds. In the case where H is real and has finite…
Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded…
We associate to each unital $C^*$-algebra $A$ a geometric object---a diagram of topological spaces representing quotient spaces of the noncommutative space underlying $A$---meant to serve the role of a generalized Gel'fand spectrum. After…
A self-adjoint operator $A$ in a Krein space $\bigl({\mathcal K},[\,\cdot\,,\cdot\,]\bigr)$ is called partially fundamentally reducible if there exist a fundamental decomposition ${\mathcal K} = {\mathcal K}_+ [\dot{+}] {\mathcal K}_-$…
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
We continue our study of the general theory of possibly nonselfadjoint algebras of operators on a Hilbert space, and modules over such algebras, developing a little more technology to connect `nonselfadjoint operator algebra' with the…
Atomic system in fuzzy Hilbert space is introduced and the existence of the fuzzy atomic systems for a strongly fuzzy bounded linear operator is studied. The notion of a K-frame in fuzzy Hilbert space is presented and some of their…
Extending the notion of parallelism we introduce the concept of approximate parallelism in normed spaces and then substantially restrict ourselves to the setting of Hilbert space operators endowed with the operator norm. We present several…
In this paper we consider A-Fredholm and semi-A-Fredholm operators on Hilbert C*-modules over a W*-algebra A defined in [3],[10]. Using the assumption that A is a W*-algebra (and not an arbitrary C*-algebra), we obtain several results such…
We discuss a few integral operators and provide expressions for them in terms of smooth functions of some natural self-adjoint operators. These operators appear in the context of scattering theory, but are independent of any perturbation…