Search results for "Operator"
showing 10 items of 1427 documents
Weyl symbols and boundedness of Toeplitz operators
2019
International audience; We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding Weyl symbols.
Noncommutative Davis type decompositions and applications
2018
We prove the noncommutative Davis decomposition for the column Hardy space $\H_p^c$ for all $0<p\leq 1$. A new feature of our Davis decomposition is a simultaneous control of $\H_1^c$ and $\H_q^c$ norms for any noncommutative martingale in $\H_1^c \cap \H_q^c$ when $q\geq 2$. As applications, we show that the Burkholder/Rosenthal inequality holds for bounded martingales in a noncommutative symmetric space associated with a function space $E$ that is either an interpolation of the couple $(L_p, L_2)$ for some $1<p<2$ or is an interpolation of the couple $(L_2, L_q)$ for some $2<q<\infty$. We also obtain the corresponding $\Phi$-moment Burkholder/Rosenthal inequality for Orlicz functions that…
Regularity of some method of summation for double sequences
2010
Some generalization of Toeplitz method of summation is introduced for double sequences and condition of regularity of it is obtained.
Unbounded C*-seminorms, biweights and *-representations of partial *-algebras: a review
2006
The notion of (unbounded) C*-seminorms plays a relevant role in the representation theory of *-algebras and partial *-algebras. A rather complete analysis of the case of *-algebras has given rise to a series of interesting concepts like that of semifinite C*-seminorm and spectral C*-seminorm that give information on the properties of *-representations of the given *-algebra A and also on the structure of the *-algebra itself, in particular when A is endowed with a locally convex topology. Some of these results extend to partial *-algebras too. The state of the art on this topic is reviewed in this paper, where the possibility of constructing unbounded C*-seminorms from certain families of p…
New applications of extremely regular function spaces
2017
Let $L$ be an infinite locally compact Hausdorff topological space. We show that extremely regular subspaces of $C_0(L)$ have very strong diameter $2$ properties and, for every real number $\varepsilon$ with $0<\varepsilon<1$, contain an $\varepsilon$-isometric copy of $c_0$. If $L$ does not contain isolated points they even have the Daugavet property, and thus contain an asymptotically isometric copy of $\ell_1$.
Weyl-Type Theorems on Banach Spaces Under Compact Perturbations
2018
In this paper, we study Browder-type and Weyl-type theorems for operators $$T+K$$ defined on a Banach space X, where K is (a non necessarily commuting) compact operator on X. In the last part, the theory is exemplified in the case of isometries, analytic Toeplitz operators, semi-shift operators, and weighted right shifts.
Algebras of frequently hypercyclic vectors
2019
We show that the multiples of the backward shift operator on the spaces $\ell_{p}$, $1\leq p<\infty$, or $c_{0}$, when endowed with coordinatewise multiplication, do not possess frequently hypercyclic algebras. More generally, we characterize the existence of algebras of $\mathcal{A}$-hypercyclic vectors for these operators. We also show that the differentiation operator on the space of entire functions, when endowed with the Hadamard product, does not possess frequently hypercyclic algebras. On the other hand, we show that for any frequently hypercyclic operator $T$ on any Banach space, $FHC(T)$ is algebrable for a suitable product, and in some cases it is even strongly algebrable.
Isometric factorization of vector measures and applications to spaces of integrable functions
2022
Let $X$ be a Banach space, $\Sigma$ be a $\sigma$-algebra, and $m:\Sigma\to X$ be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pelczýnski factorization procedure that there exist a reflexive Banach space $Y$, a vector measure $\tilde{m}:\Sigma \to Y$ and an injective operator $J:Y \to X$ such that $m$ factors as $m=J\circ \tilde{m}$. We elaborate some theory of factoring vector measures and their integration operators with the help of the isometric version of the Davis-Figiel-Johnson-Pelczýnski factorization procedure. Along this way, we sharpen a result of Okada and Ricker that if the integration operator on $L_1(m)$ is weakly compact, t…
Ein Kriterium f�r die Approximierbarkeit von Funktionen aus sobolewschen R�umen durch glatte Funktionen
1981
The present paper provides a necessary and sufficient criterion for an element of a Sobolev space W k p (Ω) to be approximated in the Sobolev norm by Ck(En)-smooth functions. Here Ω is a bounded open set of n-dimensional Euclidean space En with convex closure $$\bar \Omega$$ and boundary ∂Ω having n-dimensional Lebesgue measure zero. No further boundary regularity (such as e.g. the segment property) is required.Our main tools are the Hardy-Littlewood maximal functions and a slightly strengthened version of a well-known extension theorem of Whitney.This work was inspired by and is very close in spirit to the pertinent parts of Calderon-Zygmund [6].
The perturbation classes problem for closed operators
2017
We compare the perturbation classes for closed semi-Fredholm and Fredholm operators with dense domain acting between Banach spaces with the corresponding perturbation classes for bounded semi-Fredholm and Fredholm operators. We show that they coincide in some cases, but they are different in general. We describe several relevant examples and point out some open problems.