Multiplication operator
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On the Bohr inequality for the Cesáro operator Open
We investigate an analog of Bohr’s results for the Cesáro operator acting on the space of holomorphic functions defined on the unit disk. The asymptotical behaviour of the corresponding Bohr sum is also estimated.
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Computational Intelligence and Application of Frame Theory in Communication Systems Open
In this study, we have to discuss the reduction of noise due to peak amplitude and power ratio in multi carrier modulation scheme like Orthogonal Frequency Division Multiplexing (OFDM) process using Frame theory. The frame operator of the …
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On [m,C]-isometric operators Open
In this paper we introduce an [m;C]-isometric operator T on a complex Hilbert space H and study its spectral properties. We show that if T is an [m,C]-isometric operator and N is an n-nilpotent operator, respectively, then T + N is an [m +…
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Multiplication Operators on Cesàro Sequence Spaces Open
In this paper we characterize the compact, invertible and Fredholm multiplication operators on Cesàro sequence spaces.
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A Survey on Operator Monotonicity, Operator Convexity, and Operator Means Open
This paper is an expository devoted to an important class of real-valued functions introduced by Löwner, namely, operator monotone functions. This concept is closely related to operator convex/concave functions. Various characterizations f…
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Weighted differentiation composition operators from the logarithmic Bloch space to the weighted-type space Open
The boundedness of the weighted differentiation composition opera- tor from the logarithmic Bloch space to the weighted-type space is characterized in terms of the sequence (z n ) n∈N0 . An asymptotic estimate of the essential norm of the …
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Dynamic Mode Decomposition with Control Liouville Operators Open
This manuscript provides a theoretical foundation for the Dynamic Mode Decomposition (DMD) of control affine dynamical systems through vector valued reproducing kernel Hilbert spaces (RKHSs). Specifically, control Liouville operators and c…
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A new characterization of the generalized weighted composition operator from H^∞ into the Zygmund space Open
A new criterion for the boundedness, as well as for the compactness of the generalized weighted composition operators from H ∞ into the Zygmund space are given in this paper.
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Composition operators on the Schwartz space Open
[EN] We study composition operators on the Schwartz space of rapidly decreasing functions. We prove that such a composition operator is never a compact operator and we obtain necessary or sufficient conditions for the range of the composit…
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Resolvent Approximations in L2-Norm for Elliptic Operators Acting in a Perforated Space Open
We study homogenization of a second-order elliptic differential operator Aε = - div a(x/ε)∇ acting in an ε-periodically perforated space, where ε is a small parameter. Coefficients of the operator Aε are measurable ε-periodic functions. Th…
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Every complete Pick space satisfies the column-row property Open
In the theory of complete Pick spaces, the column-row property has appeared in a variety of contexts. We show that it is satisfied by every complete Pick space in the following strong form: each sequence of multipliers that induces a contr…
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Some inequalities involving operator monotone functions and operator means Open
In this paper we show that if f : [0,∞) → [0,∞) is an operator monotone function and A,B are positive operators such that 0 < pA B qA , then for all α ∈ [0,1]where S(t) is the so called Specht's ratio, and α is α -geometric mean.Moreover, …
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Some concrete operators and their properties Open
We consider integration and double integration operators, the Hardy operator, and multiplication and composition operators on Lebesgue space $L_{p}\left[ 0,1\right] $ and Sobolev spaces $W_{p}^{\left( n\right) }\left[ 0,1\right] $ and $W_{…
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Some Operations on Mixed Monotone Operator in Banach Spaces Open
This paper discusses some operations on mixed monotone operator in Banach space, especially addition an multiplication operations. We will prove the sum and product of two mixed monotone operators. The proof using some relevant definitions…
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Unbounded operators having self‐adjoint, subnormal, or hyponormal powers Open
We show that if a densely defined closable operator A is such that the resolvent set of A 2 is nonempty, then A is necessarily closed. This result is then extended to the case of a polynomial . We also generalize a recent result by Sebesty…
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Hilbert space operators with two-isometric dilations Open
A continuous linear Hilbert space operator S is said to be a 2-isometry if the operator S and its adjoint S∗ satisfy the relation S∗2S2−2S∗S+I=0. We study operators having liftings or dilations to 2-isometries. The adjoint of an operator w…
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Operator matrix of Moore–Penrose inverse operators on Hilbert C<sup>*</sup>-modules Open
We show that the Moore–Penrose inverse of an operator $T$ is idempotent if and only if it is a product of two projections. Furthermore, if $P$ and $Q$ are two projections, we find a relation between the entries of the associated operator m…
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Dimension free bounds for the vector-valued Hardy–Littlewood maximal operator Open
In this article, Fefferman–Stein inequalities in L^p(\mathbb R^d; \ell^q) with bounds independent of the dimension d are proved, for all 1 < p,q < +\infty . This result generalizes in a vector-valued setting the famous one by Stein for the…
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Generalized frame operator, lower semiframes, and sequences of translates Open
Given an arbitrary sequence of elements of a Hilbert space , the operator is defined as the operator associated to the sesquilinear form , for . This operator is in general different from the classical frame operator but possesses some rem…
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Embedded eigenvalues for the Neumann-Poincare operator Open
The Neumann-Poincare operator is a boundary-integral operator associated with harmonic layer potentials. This article proves the existence of eigenvalues within the essential spectrum for the Neumann-Poincar\\'e operator for certain Lipsch…
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On Operator Valued Measures Open
We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the …
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Some Generalized Euclidean Operator Radius Inequalities Open
In this work, some generalized Euclidean operator radius inequalities are established. Refinements of some well-known results are provided. Among others, some bounds in terms of the Cartesian decomposition of a given Hilbert space operator…
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Unique one-body position operator for periodic systems Open
In this work we prove that the one-body position operator for periodic systems that we have recently proposed [Phys. Rev. B 99, 205144 (2019)] is unique modulo a phase factor and an additive constant. The proof uses several general physica…
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Multiplication operators on the space of functions of bounded variation Open
In this paper,we study the properties of the multiplication operator acting on the bounded variation space BV[0, 1]. In particular,we show the existence of non-null compact multiplication operators on BV[0, 1] and non-invertible Fredholm m…
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Universal composition operators Open
A Hilbert space operator U is called \textit{universal} (in the sense of Rota) if every Hilbert space operator is similar to a multiple of U restricted to one of its invariant subspaces. It follows that the \textit{invariant subspace probl…
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Closed range weighted composition operators and dynamical sampling Open
We solve the closed range problem for weighted composition operators on Fock spaces. The result equivalently characterizes when the operators are bounded from below. We give several applications of the main result related to the operators …
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Real operator spaces and operator algebras Open
We verify that a large portion of the theory of complex operator spaces and operator algebras (as represented by the 2004 book by the author and Le Merdy for specificity) transfers to the real case. We point out some of the results that do…
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Nonseparability and von Neumann's theorem for domains of unbounded operators Open
A classical theorem of von Neumann asserts that every unbounded self-adjoint operator $A$ in a \\textit{separable} Hilbert space is unitarily equivalent to an operator $B$ such that $D(A)\\cap D(B)=\\{0\\}$. Equivalently this can be formul…
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Norm of matrix operator on Orlicz-binomial spaces and related operator ideal Open
The purpose of this article is to introduce Orlicz extension of binomial sequence spaces b r,s ϕ and investigate some topological and inclusion properties of the new spaces.We give an upper estimation of A ϕ ,b r,s ϕ , where A is the Hausd…
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Regular phase operator and SU(1,1) coherent states of the harmonic oscillator Open
A new solution is proposed to the long-standing problem of describing the\nquantum phase of a harmonic oscillator. In terms of an'exponential phase\noperator', defined by a new 'polar decomposition' of the quantized amplitude of\nthe oscil…