Moore-Penrose inverses of Gram operators on Hilbert C*-modules

M. S. Moslehian; K. Sharif; M. Forough; M. Chakoshi

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Displaying similar documents to “Moore-Penrose inverses of Gram operators on Hilbert C*-modules”

Numerical radius inequalities for Hilbert $C^{*}$ -modules

Sadaf Fakri Moghaddam, Alireza Kamel Mirmostafaee (2022)

Mathematica Bohemica

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We present a new method for studying the numerical radius of bounded operators on Hilbert $C^{*}$ -modules. Our method enables us to obtain some new results and generalize some known theorems for bounded operators on Hilbert spaces to bounded adjointable operators on Hilbert $C^{*}$ -module spaces.

Some equivalent metrics for bounded normal operators

Mohammad Reza Jabbarzadeh, Rana Hajipouri (2018)

Mathematica Bohemica

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Some stronger and equivalent metrics are defined on $ℳ$ , the set of all bounded normal operators on a Hilbert space $H$ and then some topological properties of $ℳ$ are investigated.

Some Results About Holonomic $ε$ -Modules

Jan-Erik Björk (1983)

Recherche Coopérative sur Programme n°25

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Relative tilting modules with respect to a semidualizing module

Maryam Salimi (2019)

Czechoslovak Mathematical Journal

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Let $R$ be a commutative Noetherian ring, and let $C$ be a semidualizing $R$ -module. The notion of $C$ -tilting $R$ -modules is introduced as the relative setting of the notion of tilting $R$ -modules with respect to $C$ . Some properties of tilting and $C$ -tilting modules and the relations between them are mentioned. It is shown that every finitely generated $C$ -tilting $R$ -module is $C$ -projective. Finally, we investigate some kernel subcategories related to $C$ -tilting modules.

Operators on a Hilbert space similar to a part of the backward shift of multiplicity one

Yoichi Uetake (2001)

Studia Mathematica

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Let A: X → X be a bounded operator on a separable complex Hilbert space X with an inner product $⟨ \cdot, \cdot ⟩_{X}$ . For b, c ∈ X, a weak resolvent of A is the complex function of the form $⟨ {(I - z A)}^{- 1} b, c ⟩_{X}$ . We will discuss an equivalent condition, in terms of weak resolvents, for A to be similar to a restriction of the backward shift of multiplicity 1.

Recollements induced by good (co)silting dg-modules

Rongmin Zhu, Jiaqun Wei (2023)

Czechoslovak Mathematical Journal

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Let $U$ be a dg- $A$ -module, $B$ the endomorphism dg-algebra of $U$ . We know that if $U$ is a good silting object, then there exist a dg-algebra $C$ and a recollement among the derived categories $𝐃 (C, d)$ of $C$ , $𝐃 (B, d)$ of $B$ and $𝐃 (A, d)$ of $A$ . We investigate the condition under which the induced dg-algebra $C$ is weak nonpositive. In order to deal with both silting and cosilting dg-modules consistently, the notion of weak silting dg-modules is introduced. Thus, similar results for good cosilting dg-modules are obtained....

Operator positivity and analytic models of commuting tuples of operators

Monojit Bhattacharjee, Jaydeb Sarkar (2016)

Studia Mathematica

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We study analytic models of operators of class $C_{\cdot 0}$ with natural positivity assumptions. In particular, we prove that for an m-hypercontraction $T \in C_{\cdot 0}$ on a Hilbert space , there exist Hilbert spaces and ⁎ and a partially isometric multiplier θ ∈ ℳ (H²(),A²ₘ(⁎)) such that $≅_{θ} = A ² ₘ (⁎) ⊖ θ H ² ()$ and $T ≅ P_{_{θ}} M_{z} |_{_{θ}}$ , where A²ₘ(⁎) is the ⁎-valued weighted Bergman space and H²() is the -valued Hardy space over the unit disc . We then proceed to study analytic models for doubly commuting n-tuples of operators and investigate their...

Lifting $D$ -modules from positive to zero characteristic

João Pedro P. dos Santos (2011)

Bulletin de la Société Mathématique de France

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We study liftings or deformations of $D$ -modules ( $D$ is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic $D$ -modules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given $D$ -module in positive characteristic. At the end we compare...

Generalized Hilbert Operators on Bergman and Dirichlet Spaces of Analytic Functions

Sunanda Naik, Karabi Rajbangshi (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let f be an analytic function on the unit disk . We define a generalized Hilbert-type operator $_{a, b}$ by $_{a, b} (f) (z) = Γ (a + 1) / Γ (b + 1) \int_{0}^{1} (f (t) {(1 - t)}^{b}) / ({(1 - t z)}^{a + 1}) d t$ , where a and b are non-negative real numbers. In particular, for a = b = β, $_{a, b}$ becomes the generalized Hilbert operator $_{β}$ , and β = 0 gives the classical Hilbert operator . In this article, we find conditions on a and b such that $_{a, b}$ is bounded on Dirichlet-type spaces $S^{p}$ , 0 < p < 2, and on Bergman spaces $A^{p}$ , 2 < p < ∞. Also we find an upper bound for the norm of the operator $_{a, b}$ ....

On the composition structure of the twisted Verma modules for $𝔰𝔩 (3, ℂ)$

Libor Křižka, Petr Somberg (2015)

Archivum Mathematicum

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We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra $𝔰𝔩 (3, ℂ)$ , including the explicit structure of singular vectors for both $𝔰𝔩 (3, ℂ)$ and one of its Lie subalgebras $𝔰𝔩 (2, ℂ)$ , and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as $D$ -modules on the Schubert cells in the full flag manifold for $SL (3, ℂ)$ .

Interpolation by elementary operators

Bojan Magajna (1993)

Studia Mathematica

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Given two n-tuples $a = (a_{1}, . . ., a_{n})$ and $b = (b_{1}, . . ., b_{n})$ of bounded linear operators on a Hilbert space the question of when there exists an elementary operator E such that $E a_{j} = b_{j}$ for all j =1,...,n, is studied. The analogous question for left multiplications (instead of elementary operators) is answered in any C*-algebra A, as a consequence of the characterization of closed left A-submodules in $A^{n}$ .

Stratified modules over an extension algebra

Erzsébet Lukács, András Magyar (2018)

Czechoslovak Mathematical Journal

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Let $A$ be a standard Koszul standardly stratified algebra and $X$ an $A$ -module. The paper investigates conditions which imply that the module ${Ext}_{A}^{*} (X)$ over the Yoneda extension algebra $A^{*}$ is filtered by standard modules. In particular, we prove that the Yoneda extension algebra of $A$ is also standardly stratified. This is a generalization of similar results on quasi-hereditary and on graded standardly stratified algebras.

Separable $ℵ_{k}$ -free modules with almost trivial dual

Daniel Herden, Héctor Gabriel Salazar Pedroza (2016)

Commentationes Mathematicae Universitatis Carolinae

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An $R$ -module $M$ has an almost trivial dual if there are no epimorphisms from $M$ to the free $R$ -module of countable infinite rank $R^{(ω)}$ . For every natural number $k > 1$ , we construct arbitrarily large separable $ℵ_{k}$ -free $R$ -modules with almost trivial dual by means of Shelah’s Easy Black Box, which is a combinatorial principle provable in ZFC.

A note on generalizations of semisimple modules

Engin Kaynar, Burcu N. Türkmen, Ergül Türkmen (2019)

Commentationes Mathematicae Universitatis Carolinae

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A left module $M$ over an arbitrary ring is called an $ℛ𝒟$ -module (or an $ℛ𝒮$ -module) if every submodule $N$ of $M$ with $Rad (M) \subseteq N$ is a direct summand of (a supplement in, respectively) $M$ . In this paper, we investigate the various properties of $ℛ𝒟$ -modules and $ℛ𝒮$ -modules. We prove that $M$ is an $ℛ𝒟$ -module if and only if $M = Rad (M) \oplus X$ , where $X$ is semisimple. We show that a finitely generated $ℛ𝒮$ -module is semisimple. This gives us the characterization of semisimple rings in terms of $ℛ𝒮$ -modules. We completely determine the structure...

Regularity of domains of parameterized families of closed linear operators

Teresa Winiarska, Tadeusz Winiarski (2003)

Annales Polonici Mathematici

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The purpose of this paper is to provide a method of reduction of some problems concerning families $A_{t} = {(A (t))}_{t \in}$ of linear operators with domains ${(_{t})}_{t \in}$ to a problem in which all the operators have the same domain . To do it we propose to construct a family ${(Ψ_{t})}_{t \in}$ of automorphisms of a given Banach space X having two properties: (i) the mapping $t \mapsto Ψ_{t}$ is sufficiently regular and (ii) $Ψ_{t} () =_{t}$ for t ∈ . Three effective constructions are presented: for elliptic operators of second order with the Robin boundary condition...

Extension operators on balls and on spaces of finite sets

Antonio Avilés, Witold Marciszewski (2015)

Studia Mathematica

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We study extension operators between spaces of continuous functions on the spaces $σ ₙ (2^{X})$ of subsets of X of cardinality at most n. As an application, we show that if $B_{H}$ is the unit ball of a nonseparable Hilbert space H equipped with the weak topology, then, for any 0 < λ < μ, there is no extension operator $T : C (λ B_{H}) \to C (μ B_{H})$ .

The multiplicity problem for indecomposable decompositions of modules over domestic canonical algebras

Piotr Dowbor, Andrzej Mróz (2008)

Colloquium Mathematicae

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Given a module M over a domestic canonical algebra Λ and a classifying set X for the indecomposable Λ-modules, the problem of determining the vector $m (M) = {(m_{x})}_{x \in X} \in ℕ^{X}$ such that $M ≅ ⨁_{x \in X} X_{x}^{m_{x}}$ is studied. A precise formula for $d i m_{k} H o m_{Λ} (M, X)$ , for any postprojective indecomposable module X, is computed in Theorem 2.3, and interrelations between various structures on the set of all postprojective roots are described in Theorem 2.4. It is proved in Theorem 2.2 that a general method of finding vectors m(M) presented by the authors...