Complex Analysis and Operator Theory最新文献

In a previous paper (Barrera-Castelán et al. in Bol Soc Mat Mex 27:43, 2021. https://doi.org/10.1007/s40590-021-00348-w), using disk polynomials as an orthonormal basis in the n-analytic weighted Bergman space, we showed that for every bounded radial generating symbol a, the associated Toeplitz operator, acting in this space, can be identified with a matrix sequence (gamma (a)), where the entries of the matrices are certain integrals involving a and Jacobi polynomials. In this paper, we suppose that the generating symbols a have finite limits on the boundary and prove that the C*-algebra generated by the corresponding matrix sequences (gamma (a)) is the C*-algebra of all matrix sequences having scalar limits at infinity. We use Kaplansky’s noncommutative analog of the Stone–Weierstrass theorem and some ideas from several papers by Loaiza, Lozano, Ramírez-Ortega, Ramírez-Mora, and Sánchez-Nungaray. We also prove that for (nge 2), the closure of the set of matrix sequences (gamma (a)) is not equal to the generated C*-algebra.

It is known that if the convolution of two suitably normalized planar harmonic mappings from certain families of mappings, such as those mapping into a half-plane or a strip, is locally univalent, the convolution is univalent and convex in one direction. After extending this to convolutions of mappings into a slanted half-plane with those into a slanted asymmetric strip, we prove properties for the dilatation of the convolution of a mapping from a family of slanted generalized right half-plane mappings with mappings into a slanted half-plane or a slanted asymmetric strip with a finite Blaschke product dilatation. The properties lay the foundation for a direct application of polynomial zero distribution techniques in the determination of local univalence of such convolutions. We conclude by producing a family of univalent convolutions convex in one direction between a slanted generalized right half-plane mapping and a mapping into a half-plane with a two-factor Blaschke product dilatation.

Using the Wold–von Neumann decomposition for the isometric covariant representations due to Muhly and Solel, we prove an explicit representation of the commutant of a doubly commuting pure isometric representation of the product system over (mathbb {N}_0^{k}.) As an application we study a complete characterization of invariant subspaces for a doubly commuting pure isometric representation of the product system. This provides us a complete set of isomorphic invariants. Finally, we classify a large class of an isometric covariant representations of the product system.

In a recent article, Chávez, Garcia and Hurley introduced a new family of norms (Vert cdot Vert _{{textbf {X}},d}) on the space of (n times n) complex matrices which are induced by random vectors ({textbf {X}}) having finite d-moments. Therein, the authors asked under which conditions the norms induced by a scalar multiple of ({textbf {X}}) are submultiplicative. In this paper, this question is completely answered by proving that this is always the case, as long as the entries of ({textbf {X}}) have finite p-moments for (p=max {2+varepsilon ,d}).

Abstract

We investigate the p-Carleson measure for the Bloch space ({mathcal {B}}) and introduce a holomorphic function space ( W_{mathcal {B}}^{p,alpha }) associated with this measure. An integral operator which preserves the p-Carleson measure for ({mathcal {B}}) is established. As applications, we give a generalized Jones’ formula for ( W_{mathcal {B}}^{p,alpha }) , characterize the bounded small Hankel operator (h_{s,f}) from ({mathcal {B}}) to the Bergman space (A_alpha ^p) , and give an atomic decomposition of ( W_{mathcal {B}}^{p,alpha }) .

In this short note, the second dual of generalized group algebra ((ell ^1(G,mathcal {A}),*)) equipped with both Arens product is investigated, where G is any discrete group and (mathcal {A}) is a Banach algebra containing a complemented algebraic copy of ((ell ^1(mathbb N),bullet )). We give an explicit family of annihilators(w.r.t both the Arens product) in the algebra (ell ^1(G,mathcal {A})^{**}), arising from non-principal ultrafilters on ({mathbb {N}}) and which are not in the toplogical center. As a consequence, we also deduce the fact that (ell ^1(G,mathcal {A})) is not Strongly Arens irregular.

We intend to introduce and investigate a new functional space on the quaternionic unit ball of slice hyper-meromorphic functions with unique pole at the origin. Mainly, we provide a concrete characterization of their elements and give the closed explicit expression of the associated reproducing kernel function. Moreover, we show that they are isometrically isomorphic to the configuration space on the positive real half line by means of an integral transform of Bargmann type. The closed formulas for this transform are given in two special cases.

It have been proved in Accardi and Dhahri (J Math Phys 51:2, 2010) that the set of the exponential vectors (Phi (g), ; gin {mathcal {K}}:=L^2({mathbb {R}}^d)cap L^{infty }({mathbb {R}}^d)) associated with different test functions (g_iin {mathcal {K}}), are linearly independents. Even this result is true, we present an alternative proof that is consistent with the results of this paper. In this paper, we start by a review of some results on the quadratic Fock space obtained in Accardi and Dhahri (J Math Phys 51:2, 2010) and Rebei (J Math Anal Appl 439(1): 135–153, 2016) , then we prove that the number operator is positive for non negative test function from which we deduce that the creation operator is injective. As application of the injectivity, we give an algebraic proof of the linear independence of the quadratic exponential vectors (Phi (g)).

Scalable frames in separable Hilbert spaces have been recently introduced by Kutyniok et al. to modify a general frame and to generate a Parseval frame by rescaling frame vectors. The main framework proposed in this paper is based on the redundancy of frame elements and is used as input for classification. This method leads to a complete characterization of scalable frames in (mathbb {R}^{2}) and (mathbb {R}^{3}). In addition, we introduce all possible choices for the scale coefficients of a given scalable frame. Finally, we discuss the scalability of duals frames. We divide the set of all scalable dual frames of a given frame into two disjoint subsets, containing and not containing an orthogonal basis. In particular, we prove that both of them are non-empty.

In this work, we consider the spectral problems for the Sturm–Liouville operators on a caterpillar graph with the standard matching conditions in the internal vertices and the Neumann or the Dirichlet conditions in the boundary vertices. The regularized trace formulae of these operators are established by using the residue techniques of complex analysis.