Related papers: Similarity problems, Folner sets and isometric rep…
A theorem of Siebert asserts that if a sequence of semigroups of probability measures on a Lie group G is weakly convergent to a semigroup of the same type, then the corresponding generating functionals are convergent in the weak operator…
The paper concerns algebras of almost periodic pseudodifferential operators on $\mathbb R^d$ with symbols in H\"ormander classes. We study three representations of such algebras, one of which was introduced by Coburn, Moyer and Singer and…
We undertake a systematic study of the approximation properties of the topological and measurable versions of the coarse boundary groupoid associated to a sequence of finite graphs of bounded degree. On the topological side, we prove that…
In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky-Hilbert modules over Stone algebras is established, which generalizes the well-known Hilbert space case (where it coincides with the…
We define the isoperimetric constant for any locally finite metric space and we study the property of having isoperimetric constant equal to zero. This property, called Small Neighborhood property, clearly extends amenability to any locally…
We study the existence of multiplier (completely) bounded approximate identities for the Fourier algebras of some classes of hypergroups. In particular we show that, a large class of commutative hypergroups are weakly amenable with the…
Generalizing previous work of Iwaniec, Luo, and Sarnak (2000), we use information from one-level density theorems to estimate the proportion of non-vanishing of $L$-functions in a family at a low-lying height on the critical line (measured…
In this paper we study uniform quasiconformal groups of Carnot-by-Carnot groups. We show that they can be conjugated into conformal groups provided the induced action on the space of distinct pairs is cocompact. Following the approach of…
We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
Semilinear maps are a generalization of linear maps between vector spaces where we allow the scalar action to be twisted by a ring homomorphism such as complex conjugation. In particular, this generalization unifies the concepts of linear…
Inspired by the classical category theorems of Halmos and Rohlin for the discrete measure preserving transformations, we prove analogous results in the abstract setting of unitary and isometric C_0-semigroups on a separable Hilbert space.…
Admissible vectors for unitary representations of locally compact groups are the basis for group-frame and covariant coherent state expansions. Main tools in the study of admissible vectors have been Plancherel and central integral…
We consider norms on a complex separable Hilbert space such that $\langle a\xi,\xi\rangle\leq\|\xi\|^2\leq\langle b\xi,\xi\rangle$ for positive invertible operators $a$ and $b$ that differ by an operator in the Schatten class. We prove that…
The paper discusses a series of results concerning reproducing kernel Hilbert spaces, related to the factorization of their kernels. In particular, it is proved that for a large class of spaces isometric multipliers are trivial. One also…
By using a Borel density theorem for algebraic quotients, we prove a theorem concerning isometric actions of a Lie group $G$ on a smooth or analytic manifold $M$ with a rigid $\mathrm{A}$-structure $\sigma$. It generalizes Gromov's…
The Bargmann-Fock space(or Fock space for short) is a fundamental example of reproducing kernel Hilbert spaces that has found fascinating applications across multiple fields of current interest, including quantum mechanics, time-frequency…
Let G be an amenable group, let X be a Banach space and let \pi : G --> B(X) be a bounded representation. We show that if the set {\pi(t) : t \in G} is gamma-bounded then \pi extends to a bounded homomorphism w : C*(G) --> B(X) on the group…
A study is made of linear isometries on Fr\'echet spaces for which the metric is given in terms of a sequence of seminorms. This establishes sufficient conditions on the growth of the function that defines the metric in terms of the…
K-frame theory was recently introduced to reconstruct elements from the range of a bounded linear operator K in a separable Hilbert space. This significant property is worthwhile especially in some problems arising in sampling theory. Some…