Related papers: Duality and Interpolation of Bergman Spaces

Necessary and sufficient conditions for a separable Banach space to be a dual space are proved. Some applications are discussed

In this paper we study ways to establish when a Banach space can be identified as the dual or the double dual of another Banach space. To obtain these results, we relate these spaces with other, concrete Banach spaces - tipically $\ell^1$…

Necessary and sufficient conditions for Banach space to be(isometrically isomorphic to) a dual space will be given.

If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A_0,A_1) such that A_0 and A_1 are isometric to $X\oplus V$, and any intermediate space obtained using the…

First, we consider some fundamental properties including dual spaces, complex interpolations of $\alpha$-modulation spaces $M^{s,\alpha}_{p,q}$ with $0<p,q \le \infty$. Next, necessary and sufficient conditions for the scaling property and…

Most characterizations of interpolating sequences for Bergman spaces include the condition that the sequence be uniformly discrete in the hyperbolic metric. We show that if the notion of interpolation is suitably generalized, two of these…

We prove that the dual of an M ideal of a Banach space inherits all the versions of $w^*$ diameter two properties. We give a counter example to show that the converse is not true. We use these results to explore these properties in $C(K)$…

The aim of the paper is to establish duals of the limiting real interpolation $K$- and $J$-spaces $(X_0,X_1)_{0,q,v;K}$ and $(X_0,X_1)_{0,q,v;J}$, where $(X_0,X_1)$ is a compatible couple of Banach spaces, $1\le q<\infty$, $v$ is a slowly…

Given a set $B$ of operators between subspaces of $L_p$ spaces, we characterize the operators between subspaces of $L_p$ spaces that remain bounded on the $X$-valued $L_p$ space for every Banach space on which elements of the original class…

For a real normed space $X$, we study the $n$-dual space of $\left(X,\left\Vert \cdot \right\Vert \right) $ and show that the space is a Banach space. Meanwhile, for a real normed space $X$ of dimension $d\geq n$ which satisfies property…

Expected duality and approximation properties are shown to fail on Bergman spaces of domains in $\mathbb{C}^n$, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation…

We construct an example of a real Banach space whose group of surjective isometries has no uniformly continuous one-parameter semigroups, but the group of surjective isometries of its dual contains infinitely many of them. Other examples…

Let X be a complex Banach space, in this work we characterize the property of Frechet differentiability for the dual space of X. In the following, we show that if the dual space of X is Gateaux differentiable, then the dual space of Lp(X)…

We present a unified approach to the processes of inversion and duality for quasilinear and $1$-quasilinear maps; in particular, for centralizers and differentials generated by interpolation methods.

The duality of uniform approximation property for Banach spaces is well known. In this note, we establish, under the assumption of local reflexivity, the duality of uniform approximation property in the category of operator spaces.

We introduce the notion of common retraction and coretraction for families of Banach spaces, formulate a framework for identifying interpolation spaces, and apply it to modulation spaces with exponential weights $E^s_{p,q}$. By constructing…

We present the abstract framework and some applications of interpolation theory. The main new result concerns interpolation between H^1 and L^p estimates for analytic families of operators acting on Schwartz functions.

We study the double iterated outer $L^p$ spaces, namely the outer $L^p$ spaces associated with three exponents and defined on sets endowed with a measure and two outer measures. We prove that in the case of finite sets, under certain…

The requirement of an $SL(2)$ duality symmetry, mixing the worldvolume field equations with Bianchi identities, leads to a highly nonlinear equation involving the transformation parameters and certain worldvolume currents. In general, this…

We study the geometry of equiclassical strata of the discriminant in the space of plane curves of a given degree, which are families of curves of given degree, genus and class (degree of the dual curve). Our main observation is that the use…