Smooth operators in the commutant of a contraction

Pascale Vitse

Displaying similar documents to “Smooth operators in the commutant of a contraction”

Multiple summing operators on $l_{p}$ spaces

Dumitru Popa (2014)

Studia Mathematica

Similarity:

We use the Maurey-Rosenthal factorization theorem to obtain a new characterization of multiple 2-summing operators on a product of $l_{p}$ spaces. This characterization is used to show that multiple s-summing operators on a product of $l_{p}$ spaces with values in a Hilbert space are characterized by the boundedness of a natural multilinear functional (1 ≤ s ≤ 2). We use these results to show that there exist many natural multiple s-summing operators $T : l_{4 / 3} \times l_{4 / 3} \to l ₂$ such that none of the associated linear operators...

Isomorphic properties in spaces of compact operators

Ioana Ghenciu (2023)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We introduce the definition of $p$ -limited completely continuous operators, $1 \leq p < \infty$ . The question of whether a space of operators has the property that every $p$ -limited subset is relative compact when the dual of the domain and the codomain have this property is studied using $p$ -limited completely continuous evaluation operators.

The Embeddability of c₀ in Spaces of Operators

Ioana Ghenciu, Paul Lewis (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

Results of Emmanuele and Drewnowski are used to study the containment of c₀ in the space $K_{w *} (X *, Y)$ , as well as the complementation of the space $K_{w *} (X *, Y)$ of w*-w compact operators in the space $L_{w *} (X *, Y)$ of w*-w operators from X* to Y.

On hyponormal operators in Krein spaces

Kevin Esmeral, Osmin Ferrer, Jorge Jalk, Boris Lora Castro (2019)

Archivum Mathematicum

Similarity:

In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators $T$ for which there exists a fundamental decomposition $𝕂 = 𝕂^{+} \oplus 𝕂^{-}$ of the Krein space $𝕂$ with $𝕂^{+}$ and $𝕂^{-}$ invariant under $T$ .

Regularity of domains of parameterized families of closed linear operators

Teresa Winiarska, Tadeusz Winiarski (2003)

Annales Polonici Mathematici

Similarity:

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...

On a proof of the boundedness and nuclearity of pseudodifferential operators in $R^{n}$

Jan A. Rempała (1990)

Annales Polonici Mathematici

Similarity:

Absolutely continuous linear operators on Köthe-Bochner spaces

(2011)

Banach Center Publications

Similarity:

Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let $(X, | | \cdot | |_{X})$ and $(Y, | | \cdot | |_{Y})$ be real Banach spaces. A linear operator T acting from the Köthe-Bochner space E(X) to Y is said to be absolutely continuous if $| | T (1_{A ₙ} f) {| |}_{Y} \to 0$ whenever μ(Aₙ) → 0, (Aₙ) ⊂ Σ. In this paper we examine absolutely continuous operators from E(X) to Y. Moreover, we establish relationships between different classes of linear operators from E(X) to Y.

Interpolation by elementary operators

Bojan Magajna (1993)

Studia Mathematica

Similarity:

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 $A^{n}$ .

Unitary equivalence and decompositions of finite systems of closed densely defined operators in Hilbert spaces

Piotr Niemiec

Similarity:

An ideal of N-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with respect to ideals) for N-tuples of closed densely defined linear operators acting in a common (arbitrary) Hilbert space are presented. Algebraic and order (with respect to containment) properties of the class $C D D_{N}$ of all unitary equivalence classes of such N-tuples...

Operator $e^{- λ s^{α}}$

A. Takači (1978)

Matematički Vesnik

Similarity:

Compact operators whose adjoints factor through subspaces of $l_{p}$

Deba P. Sinha, Anil K. Karn (2002)

Studia Mathematica

Similarity:

For p ≥ 1, a subset K of a Banach space X is said to be relatively p-compact if $K \subset \sum_{n = 1}^{\infty} α ₙ x ₙ : α ₙ \in B a l l (l_{p^{'}})$ , where p’ = p/(p-1) and $x ₙ \in l_{p}^{s} (X)$ . An operator T ∈ B(X,Y) is said to be p-compact if T(Ball(X)) is relatively p-compact in Y. Similarly, weak p-compactness may be defined by considering $x ₙ \in l_{p}^{w} (X)$ . It is proved that T is (weakly) p-compact if and only if T* factors through a subspace of $l_{p}$ in a particular manner. The normed operator ideals $(K_{p}, κ_{p})$ of p-compact operators and $(W_{p}, ω_{p})$ of weakly p-compact operators, arising from these factorizations,...

Generalized Cesàro operators on certain function spaces

Sunanda Naik (2010)

Annales Polonici Mathematici

Similarity:

Motivated by some recent results by Li and Stević, in this paper we prove that a two-parameter family of Cesàro averaging operators $^{b, c}$ is bounded on the Dirichlet spaces $_{p, a}$ . We also give a short and direct proof of boundedness of $^{b, c}$ on the Hardy space $H^{p}$ for 1 < p < ∞.

$H^{\infty}$ functional calculus for sectorial and bisectorial operators

Giovanni Dore, Alberto Venni (2005)

Studia Mathematica

Similarity:

We give a concise exposition of the basic theory of $H^{\infty}$ functional calculus for N-tuples of sectorial or bisectorial operators, with respect to operator-valued functions; moreover we restate and prove in our setting a result of N. Kalton and L. Weis about the boundedness of the operator $f (T ₁, . . ., T_{N})$ when f is an R-bounded operator-valued holomorphic function.

Spaces of compact operators on $C (2^{} \times [0, α])$ spaces

Elói Medina Galego (2011)

Colloquium Mathematicae

Similarity:

We classify, up to isomorphism, the spaces of compact operators (E,F), where E and F are the Banach spaces of all continuous functions defined on the compact spaces $2^{} \times [0, α]$ , the topological products of Cantor cubes $2^{}$ and intervals of ordinal numbers [0,α].

Optimal Constants in Khintchine Type Inequalities for Fermions, Rademachers and q-Gaussian Operators

Artur Buchholz (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

For $(P_{k})$ being Rademacher, Fermion or q-Gaussian (-1 ≤ q ≤ 0) operators, we find the optimal constants $C_{2 n}$ , n∈ ℕ, in the inequality $∥ \sum_{k = 1}^{N} A_{k} \otimes P_{k} ∥_{2 n} \leq {[C_{2 n}]}^{1 / 2 n} m a x {∥ (\sum_{k = 1}^{N} A *_{k} A_{k}}^{1 / 2} ∥_{L_{2 n}}, ∥ (\sum_{k = 1}^{N} A_{k} A *_{k}$ 1/2∥L2n $,$ valid for all finite sequences of operators $(A_{k})$ in the non-commutative $L_{2 n}$ space related to a semifinite von Neumann algebra with trace. In particular, $C_{2 n} = (2 n r - 1)!!$ for the Rademacher and Fermion sequences.

Subharmonicity in von Neumann algebras

Thomas Ransford, Michel Valley (2005)

Studia Mathematica

Similarity:

Let ℳ be a von Neumann algebra with unit $1_{ℳ}$ . Let τ be a faithful, normal, semifinite trace on ℳ. Given x ∈ ℳ, denote by $μ_{t} {(x)}_{t \geq 0}$ the generalized s-numbers of x, defined by $μ_{t} (x)$ = inf||xe||: e is a projection in ℳ i with $τ (1_{ℳ} - e)$ ≤ t (t ≥ 0). We prove that, if D is a complex domain and f:D → ℳ is a holomorphic function, then, for each t ≥ 0, $λ \mapsto \int_{0}^{t} l o g μ_{s} (f (λ)) d s$ is a subharmonic function on D. This generalizes earlier subharmonicity results of White and Aupetit on the singular values of matrices.

Order bounded composition operators on the Hardy spaces and the Nevanlinna class

Nizar Jaoua (1999)

Studia Mathematica

Similarity:

We study the order boundedness of composition operators induced by holomorphic self-maps of the open unit disc D. We consider these operators first on the Hardy spaces $H^{p}$ 0 < p < ∞ and then on the Nevanlinna class N. Given a non-negative increasing function h on [0,∞[, a composition operator is said to be X,Lh-order bounded (we write (X,Lh)-ob) with $X = H^{p}$ or X = N if its composition with the map f ↦ f*, where f* denotes the radial limit of f, is order bounded from X into $L_{h}$ . We give...

Representing non-weakly compact operators

Manuel González, Eero Saksman, Hans-Olav Tylli (1995)

Studia Mathematica

Similarity:

For each S ∈ L(E) (with E a Banach space) the operator R(S) ∈ L(E**/E) is defined by R(S)(x** + E) = S**x** + E(x** ∈ E**). We study mapping properties of the correspondence S → R(S), which provides a representation R of the weak Calkin algebra L(E)/W(E) (here W(E) denotes the weakly compact operators on E). Our results display strongly varying behaviour of R. For instance, there are no non-zero compact operators in Im(R) in the case of $L^{1}$ and C(0,1), but R(L(E)/W(E)) identifies isometrically...

Extension operators on balls and on spaces of finite sets

Antonio Avilés, Witold Marciszewski (2015)

Studia Mathematica

Similarity:

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 natural linear operators $T * ⇝ T T^{(r)}$

J. Kurek, W. M. Mikulski (2003)

Colloquium Mathematicae

Similarity:

For natural numbers n ≥ 3 and r a complete description of all natural bilinear operators $T * \times_{ℳ f ₙ} T^{(0, 0)} ⇝ T^{(0, 0)} T^{(r)}$ is presented. Next for natural numbers r and n ≥ 3 a full classification of all natural linear operators $T *_{| ℳ f ₙ} ⇝ T T^{(r)}$ is obtained.

On extensions of families of operators

Oleg Lihvoinen (2023)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The strong closure of feasible states of families of operators is studied. The results are obtained for self-adjoint operators in reflexive Banach spaces and for more concrete case - families of elliptic systems encountered in the optimal layout of $r$ materials. The results show when it is possible to parametrize the strong closure by the same type of operators. The results for systems of elliptic operators for the case when number of unknown functions $m$ is less than the dimension $n$ of...

Some equivalent metrics for bounded normal operators

Mohammad Reza Jabbarzadeh, Rana Hajipouri (2018)

Mathematica Bohemica

Similarity:

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.

On a Kleinecke-Shirokov theorem

Vasile Lauric (2021)

Czechoslovak Mathematical Journal

Similarity:

We prove that for normal operators $N_{1}, N_{2} \in ℒ (ℋ),$ the generalized commutator $[N_{1}, N_{2}; X]$ approaches zero when $[N_{1}, N_{2}; [N_{1}, N_{2}; X]]$ tends to zero in the norm of the Schatten-von Neumann class $𝒞_{p}$ with $p > 1$ and $X$ varies in a bounded set of such a class.

Best approximation in spaces of bounded linear operators

Grzegorz Lewicki

Similarity:

CONTENTSChapter 0...............................................................................................................................................................................5 0.1. Introduction..................................................................................................................................................................5 0.2. Preliminary results.......................................................................................................................................................9Chapter...