Related papers: Schauder Bases and Operator Theory

We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…

We consider various notions of equivalence in the space of bounded operators on a Hilbert space, in particular modulo finite rank, modulo Schatten $p$-class, and modulo compact. Using Hjorth's theory of turbulence, the latter two are shown…

We generalize some results on compact operators on Hilbert spaces to "compact" operators on some Hilbert right W*-modules. We present in this frame the Schatten decomposition of the compact operators, the trace, the Banach Lp-spaces and…

This is a companion to recent papers of the authors; here we construct the `noncommutative Shilov boundary' of a (possibly nonunital) selfadjoint ordered space of Hilbert space operators. The morphisms in the universal property of the…

The aim of this note is to introduce a compound basis for the space of symmetric functions. Our basis consists of products of Schur functions and $Q$-functions. The basis elements are indexed by the partitions. It is well known that the…

We introduce new techniques allowing one to construct diagonals of bounded Hilbert space operators and operator tuples under "Blaschke-type" assumptions. This provides a new framework for a number of results in the literature and…

The aim of this paper is to study when two composition operators on the Hilbert space of Dirichlet series with square summable coefficients belong to the same component or when their difference is compact. As a corollary we show that if a…

We establish global Schauder estimates for integro-partial differential equations (IPDE) driven by a possibly degenerate L\'evy Ornstein-Uhlenbeck operator, both in the elliptic and parabolic setting, using some suitable anisotropic…

We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems through systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…

Let $\mathcal{H}$ be a (separable) Hilbert space and $\{e_k\}_{k\geq 1}$ a fixed orthonormal basis of $\mathcal{H}$. Motivated by many papers on scaled projections, angles of subspaces and oblique projections, we define and study the notion…

Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…

We give a generalization of the Hodge operator to spaces $(V,h)$ endowed with a hermitian or symmetric bilinear form $h$ over arbitrary fields, including the characteristic two case. Suitable exterior powers of $V$ become free modules over…

We consider linear second order nonvariational partial differential operators of the kind a_{ij}X_{i}X_{j}+X_{0}, on a bounded domain of R^{n}, where the X_{i}'s (i=0,1,2,...,q, n>q+1) are real smooth vector fields satisfying H\"ormander's…

We construct a topology on the standard Hilbert module $l^2(\mathcal A)$ over a unital $W^*$-algebra $\mathcal A$ such that any "compact" operator, (i.e.\ any operator in the norm closure of the linear span of the operators of the form…

We construct a Hereditarily Indecomposable Banach space $\eqs_d$ with a Schauder basis \seq{e}{n} on which there exist strictly singular non-compact diagonal operators. Moreover, the space $\mc{L}_{\diag}(\eqs_d)$ of diagonal operators with…

A new technique for proving fixed point theorems for families of holomorphic transformations of operator balls is developed. One of these theorems is used to show that a bounded representation in a real or complex Hilbert space is…

In a recent contribution we showed that there exists a smooth, dense domain for singular potential Schr\"odinger operators on the real line which is invariant under taking derivatives of arbitrary order and under multiplication by positive…

We present a general framework of localized operators, i.e., operators whose matrix coefficients with respect to the Gabor frame are concentrated on the diagonal. We show that localized operators are bounded between modulation spaces, and…

We show that the unitary operator on a separable Hilbert space is a parametrization of any conditional probability measure in a standard measure space. We propose unitary inference, a generalization of Bayesian inference. We study…

It is shown that a pair of Hilbert space operators V and W such that V*W=I (called a biisometric pair) shares some common properties with unilateral shifts when orthonormal basis are replaced with biorthogonal sequences, and it is also…