Related papers: Geometric constructions of thin Blaschke products …
A real semi-inner-product space is a real vector space $\M$ equipped with a function $[.,.] : \M \times \M \to \Re$ which is linear in its first variable, strictly positive and satisfies the Schwartz inequality. It is well-known that the…
The relationship between the distribution of zeros of an infinite Blaschke product $B$ and the inclusion in weighted Bergman spaces $A_{\alpha}^p$ of the derivative of $B$ or the derivative of functions in its model space $H^2 \ominus BH^2$…
In this paper, we study the product BMO space, little bmo space and their connections with the corresponding commutators associated with Bessel operators studied by Weinstein, Huber, and by Muckenhoupt-Stein. We first prove that the product…
The Bohr compactification is a well known construction for (topological) groups and semigroups. Recently, this notion has been investigated for arbitrary structures in \cite{har_kun:bohr_discrete} where the Bohr compactification is defined,…
Let $B(z)$ be a finite Blaschke product of degree $n$. We consider the problem when a finite Blaschke product can be written as a composition of two nontrivial Blaschke products of lower degree related to the condition $% B\circ M=B$ where…
We introduce multidimensional Schur multipliers and characterise them generalising well known results by Grothendieck and Peller. We define a multidimensional version of the two dimensional operator multipliers studied recently by Kissin…
We observe that local embedding problems for certain Hardy and Bergman spaces of Dirichlet series are equivalent to boundedness of a class of composition operators. Following this, we perform a careful study of such composition operators…
In this paper the necessary and sufficient conditions for the product of composition operators to be isometry are obtained on weighted Bergman space. With the help of a counter example we also proved that unlike on…
A closed subspace $\mathcal{M}$ of the Hardy space $H^2(\mathbb{D}^2)$ over the bidisk is called a submodule if it is invariant under multiplication by coordinate functions $z_1$ and $z_2$. Whether every finitely generated submodule is…
In this paper, we study \lambda-biharmonic hypersurfaces in the product space L^{m}\times\mathbb{R}, where L^{m} is an Einstein space and \mathbb{R} is a real line. We prove that \lambda-biharmonic hypersurfaces with constant mean curvature…
We study reducing subspaces for an analytic multiplication operator M_{z^{n}} on the Bergman space L_{a}^{2}(A_{r}) of the annulus A_{r}, and we prove that M_{z^{n}} has exactly 2^n reducing subspaces. Furthermore, in contrast to what…
Let $ E $ be a space of holomorphic functions on the unit ball $ B_X $ of a Banach space $ X.$ In this work, we introduce a Banach structure associated to $ E $ on the linear space $ WE(Y) $ containing $ Y$-valued holomorphic functions on $…
Let $\mathscr{H}^2$ denote the space of ordinary Dirichlet series with square summable coefficients, and let $\mathscr{H}^2_0$ denote its subspace consisting of series vanishing at $+\infty$. We investigate the weak product spaces…
Let M be a surface (possibly nonorientable) with punctures and/or boundary components. The paper is a study of ``geometric subgroups'' of the mapping class group of M, that is subgroups corresponding to inclusions of subsurfaces (possibly…
In this paper we study some geometric properties like parallelism, orthogonality and semi-rotundity in the space of bounded linear operators. We completely characterize parallelism of two compact linear operators between normed linear…
A broader class of Hardy spaces and Lebesgue spaces have been introduced recently on the unit circle by considering continuous $\|.\|_1$-dominating normalized gauge norms instead of the classical norms on measurable functions and a Beurling…
Suppose that $f := (f_1,\ldots,f_d):\Omega_1\to\Omega_2$ is a proper holomorphic map between two bounded domains in $\mathbb C^d.$ In this paper, we find a non-trivial minimal joint reducing subspace for the multiplication operator (tuple)…
The Lipschitz space of an infinite (locally-finite) graph is defined as the set of functions on the vertices of the graph such that the differences of the values between adjacent vertices remain bounded. In this paper we prove that this set…
We present some results related to Hahn-Banach extension theorem for linear operators on asymmetric normed spaces. L. Nachbin, Trans. Amer. Math. Soc. 68 (1950), proved that a Banach space has the extension property for linear operators (a…
Let $(M,\Gamma)$ be a Hopf--von Neumann algebra, so that $M_\ast$ is a completely contractive Banach algebra. We investigate whether the product of two elements of $M$ that are both weakly almost periodic functionals on $M_\ast$ is again…