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

Yoichi Uetake

Displaying similar documents to “Operators on a Hilbert space similar to a part of the backward shift of multiplicity one”

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 $T : C (λ B_{H}) \to C (μ B_{H})$ .

On the separation properties of $K_{ω}$

Malgorzata Wójcicka (1986)

Colloquium Mathematicae

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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.

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 isometrical extension properties of function spaces

Hisao Kato (2015)

Commentationes Mathematicae Universitatis Carolinae

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In this note, we prove that any “bounded” isometries of separable metric spaces can be represented as restrictions of linear isometries of function spaces $C (Q)$ and $C (Δ)$ , where $Q$ and $Δ$ denote the Hilbert cube ${[0, 1]}^{\infty}$ and a Cantor set, respectively.

Borel parts of the spectrum of an operator and of the operator algebra of a separable Hilbert space

Piotr Niemiec (2012)

Studia Mathematica

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For a linear operator T in a Banach space let $σ_{p} (T)$ denote the point spectrum of T, let $σ_{p, n} (T)$ for finite n > 0 be the set of all $λ \in σ_{p} (T)$ such that dim ker(T - λ) = n and let $σ_{p, \infty} (T)$ be the set of all $λ \in σ_{p} (T)$ for which ker(T - λ) is infinite-dimensional. It is shown that $σ_{p} (T)$ is $ℱ_{σ}$ , $σ_{p, \infty} (T)$ is $ℱ_{σ δ}$ and for each finite n the set $σ_{p, n} (T)$ is the intersection of an $ℱ_{σ}$ set and a $_{δ}$ set provided T is closable and the domain of T is separable and weakly σ-compact. For closed densely defined operators in a separable Hilbert space a more...

Hilbert series of the Grassmannian and $k$ -Narayana numbers

Lukas Braun (2019)

Communications in Mathematics

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We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods. This is made possible by showing that the denominator of the $q$ -Hilbert series is a Vandermonde-like determinant. We show that the $h$ -polynomial of the Grassmannian coincides with the $k$ -Narayana polynomial. A simplified formula for the $h$ -polynomial of Schubert varieties is given. Finally, we use a generalized hypergeometric Euler transform to find simplified formulae for the $k$ -Narayana numbers,...

The subspace of weak $P$ -points of $ℕ^{*}$

Salvador García-Ferreira, Y. F. Ortiz-Castillo (2015)

Commentationes Mathematicae Universitatis Carolinae

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Let $W$ be the subspace of $ℕ^{*}$ consisting of all weak $P$ -points. It is not hard to see that $W$ is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that $W$ is a $p$ -pseudocompact space for all $p \in ℕ^{*}$ .

Perturbations of real parts of eigenvalues of bounded linear operators in a Hilbert space

Michael Gil' (2024)

Czechoslovak Mathematical Journal

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Let $A$ be a bounded linear operator in a complex separable Hilbert space $ℋ$ , and $S$ be a selfadjoint operator in $ℋ$ . Assuming that $A - S$ belongs to the Schatten-von Neumann ideal $𝒮_{p}$ $(p > 1),$ we derive a bound for $\sum_{k} {| R λ_{k} (A) - λ_{k} (S) |}^{p}$ , where $λ_{k} (A)$ $(k = 1, 2, \dots)$ are the eigenvalues of $A$ . Our results are formulated in terms of the “extended” eigenvalue sets in the sense introduced by T. Kato. In addition, in the case $p = 2$ we refine the Weyl inequality between the real parts of the eigenvalues of $A$ and the eigenvalues...

On the range-kernel orthogonality of elementary operators

Said Bouali, Youssef Bouhafsi (2015)

Mathematica Bohemica

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Let $L (H)$ denote the algebra of operators on a complex infinite dimensional Hilbert space $H$ . For $A, B \in L (H)$ , the generalized derivation $δ_{A, B}$ and the elementary operator $Δ_{A, B}$ are defined by $δ_{A, B} (X) = A X - X B$ and $Δ_{A, B} (X) = A X B - X$ for all $X \in L (H)$ . In this paper, we exhibit pairs $(A, B)$ of operators such that the range-kernel orthogonality of $δ_{A, B}$ holds for the usual operator norm. We generalize some recent results. We also establish some theorems on the orthogonality of the range and the kernel of $Δ_{A, B}$ with respect to the wider class of unitarily invariant...

Generalization of the weak amenability on various Banach algebras

Madjid Eshaghi Gordji, Ali Jabbari, Abasalt Bodaghi (2019)

Mathematica Bohemica

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The generalized notion of weak amenability, namely $(ϕ, ψ)$ -weak amenability, where $ϕ, ψ$ are continuous homomorphisms on a Banach algebra $𝒜$ , was introduced by Bodaghi, Eshaghi Gordji and Medghalchi (2009). In this paper, the $(ϕ, ψ)$ -weak amenability on the measure algebra $M (G)$ , the group algebra $L^{1} (G)$ and the Segal algebra $S^{1} (G)$ , where $G$ is a locally compact group, are studied. As a typical example, the $(ϕ, ψ)$ -weak amenability of a special semigroup algebra is shown as well.

On varieties of Hilbert type

Lior Bary-Soroker, Arno Fehm, Sebastian Petersen (2014)

Annales de l’institut Fourier

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A variety $X$ over a field $K$ is of Hilbert type if $X (K)$ is not thin. We prove that if $f : X \to S$ is a dominant morphism of $K$ -varieties and both $S$ and all fibers $f^{- 1} (s)$ , $s \in S (K)$ , are of Hilbert type, then so is $X$ . We apply this to answer a question of Serre on products of varieties and to generalize a result of Colliot-Thélène and Sansuc on algebraic groups.