In this note, we show that quasi-free Hilbert modules R defined over natural function algebras satisfying a certain positivity condition, defined via the hereditary functional calculus, admit a dilation (actually a co-extension) to the Hardy module over the polydisk. An explicit realization of the dilation space is given along with the isometric embedding of the module R in it. Some consequence...

The operator-valued Schur-class is defined to be the set of holomorphic functions S mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of alternate characterizations: the operator of multiplication by S defines a contraction operator between two Hardy Hilbert spaces, S satisfies a von Neumann inequality, a certain operator-valued kernel ...

In this note, we show that quasi-free Hilbert modules R defined over the polydisk algebra satisfying a certain positivity condition, defined via the hereditary functional calculus, admit a unique minimal dilation (actually a co-extension) to the Hardy module over the polydisk. An explicit realization of the dilation space is given along with the isometric embedding of the module R in it. Some c...

‎Given a compact space $X$ and a commutative Banach algebra‎ ‎$A$‎, ‎the character spaces of $A$-valued function algebras on $X$ are‎ ‎investigated‎. ‎The class of natural $A$-valued function algebras‎, ‎those whose characters can be described by means of characters of $A$ and‎ ‎point evaluation homomorphisms‎, ‎is introduced and studied‎. ‎For an‎ ‎admissible Banach $A$-valued function algebra...

$top$-filters can be used to define $top$-convergence spaces in the lattice-valued context. Connections between $top$-convergence spaces and lattice-valued convergence spaces are given. Regularity of a $top$-convergence space has recently been defined and studied by Fang and Yue. An equivalent characterization is given in the present work in terms of convergence of closures of $top$-filters.  M...

Let ( X , ρ μ ) $({\mathcal {X}},\rho ,\mu )$ be a space of homogeneous type in the sense Coifman and Weiss, let Y $Y({\mathcal {X}})$ ball quasi-Banach function on ${\mathcal {X}}$ which supports both Fefferman–Stein vector-valued maximal inequality boundedness powered Hardy–Littlewood operator its associate space. The authors first introduce Hardy H ∗ $H_{Y}^*({\mathcal associated with via gr...

Let H 2 ( D n ) denote the Hardy space over polydisc , ≥ . A closed subspace Q ⊆ is called Beurling quotient module if there exists an inner function θ ∈ ∞ such that = / We present a complete characterization of modules : be subspace, and let C z i P M | 1 … Then only I − ⁎ j 0 ≠ two applications: first, we obtain dilation theorem for Brehmer -tuples commuting contractions, and, second, relate ...

In this paper we consider the so called a vector metric space, which is a generalization of metric space, where the metric is Riesz space valued. We prove some common fixed point theorems for three mappings in this space. Obtained results extend and generalize well-known comparable results in the literature.

Free interpolation in Hardy spaces is caracterized by the well-known Carleson condition. The result extends to Hardy-Orlicz spaces contained in the scale of classical Hardy spaces H, p > 0. For the Smirnov and the Nevanlinna classes, interpolating sequences have been characterized in a recent paper in terms of the existence of harmonic majorants (quasi-bounded in the case of the Smirnov class)....