Related papers: From graph to Riesz continuity

We introduce and study certain topological spaces associated with connected rooted graphs. These spaces reflect combinatorial and order theoretic properties of the underlying graph and relate in the case of hyperbolic graphs to Gromov's…

Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space L(H) of linear bounded operators on H with weak operator topology. We prove that if U is a measurable map from G to L(H) then it…

We present a Riesz integral representation theory in which functions, operators and measures take values in uniform commutative monoids (a commutative monoid with a uniformity making the binary operation of the monoid uniformly continuous).…

Let (X j , d j , $\mu$ j), j = 0, 1,. .. , m be metric measure spaces. Given 0 < p $\kappa$ $\le$ $\infty$ for $\kappa$ = 1,. .. , m and an analytic family of multilinear operators T z : L p 1 (X 1) x $\bullet$ $\bullet$ $\bullet$ L p m (X…

Let $E$ and $F$ be Hilbert $C^*$-modules over a $C^*$-algebra $\CAlg{A}$. New classes of (possibly unbounded) operators $t:E\to F$ are introduced and investigated. Instead of the density of the domain $\Def(t)$ we only assume that $t$ is…

The image of a given orthonormal basis for a separable Hilbert space $\mathcal{H}$ under a bijective, bounded, and linear operator acting on $\mathcal{H}$ is called a Riesz basis of $\mathcal{H}$. Contrary to what happens with Riesz bases…

Let $\A$ and $\B$ be operator algebras with $c_0$-isomorphic diagonals and let $\K$ denote the compact operators. We show that if $\A\otimes\K$ and $\B\otimes\K$ are isometrically isomorphic, then $\A$ and $\B$ are isometrically isomorphic.…

It is known that a continuous family of compact operators can be diagonalized pointwise. One can consider this fact as a possibility of diagonalization of the compact operators in Hilbert modules over a commutative W*-algebra. The aim of…

In the first half of this text we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch & Silbermann and Lindner) and the concepts and results of the generalised…

We prove that the Heisenberg Riesz transform is $L_2$--unbounded on a family of intrinsic Lipschitz graphs in the first Heisenberg group $\mathbb{H}$. We construct this family by combining a method from \cite{NY2} with a stopping time…

We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle $\GR$ of Lie groups. If the fibers of $\GR \to B$ are simply-connected solvable, we then compute the Chern…

We show how the Atiyah-Singer family index theorem for both, usual and self-adjoint elliptic operators fits naturally into the framework of the Madsen-Tillmann-Weiss spectra. Our main theorem concerns bundles of odd-dimensional manifolds.…

The conditions for sequences $\{f_{k}\}_{k=1}^{\infty}$ and $\{g_{k}\}_{k=1}^{\infty}$ being Bessel sequences, frames or Riesz bases, can be expressed in terms of the so-called cross-Gram matrix. In this paper we investigate the cross-Gram…

Let $\mathcal{G}$ be a countably infinite group of unitary operators on a complex separable Hilbert space $H$. Let $X = \{x_{1},...,x_{r}\}$ and $Y = \{y_{1},...,y_{s}\}$ be finite subsets of $H$, $r < s$, $V_{0} = \bar{span}…

In this article, we give conditions on a graph under which the Lov\'{a}sz' original bound of the graph can be improved by increasing the topological connectivity of its neighbourhood complex. We also work out conditions under which…

An example due to Pisier shows that two commuting, completely polynomially bounded Hilbert space operators may not be simultaneously similar to contractions. Thus, while each operator is individually similar to a contraction, the pair is…

We prove that if a Bessel sequence in a Hilbert space, that is indexed by a countably infinite group in an invariant manner, can be partitioned into finitely many Riesz basic sequences, then each of the sets in the partition can be chosen…

This note deals with the operator $T^*T$, where $T$ is a densely defined operator on a complex Hilbert space. We reprove a recent result of Z. Sebesty\'en and Zs. Tarcsay [13]: If $T^*T$ and $TT^*$ are self-adjoint, then $T$ is closed. In…

A family of algebras, which we call topological conjugacy algebras, is associated with each proper continuous map on a locally compact Hausdorff space. Assume that $\eta_i:\X_i\to \X_i$ is a continuous proper map on a locally compact…

We associate to a parametrized family $f$ of nonlinear Fredholm maps possessing a trivial branch of zeroes an {\it index of bifurcation} $\beta(f)$ which provides an algebraic measure for the number of bifurcation points from the trivial…