Related papers: Semi-regular biorthogonal pairs and generalized Ri…
The purpose of this article is twofold. First of all, the notion of $(D, E)$-quasi basis is introduced for a pair $(D, E)$ of dense subspaces of Hilbert spaces. This consists of two biorthogonal sequences $\{ \varphi_n \}$ and $\{ \psi_n…
Pseudo-Hermitian Hamiltonians have recently become a field of wide investigation. Originally, the Generalized Riesz Systems (GRS) have been introduced as an auxiliary tool in this theory. In contrast, the current paper, GRSs are analysed in…
In this note we prove that if two Riesz-Fischer sequences in a separable Hilbert space $H$ are biorthogonal and one of them is complete in $H$, then both sequences are Riesz bases for $H$. This complements a recent result by D. T. Stoeva…
We construct a two-parameters example of {\em pseudo-bosons}, and we show that they are not regular, in the sense previously introduced by the author. In particular, we show that two biorthogonal bases of $\Lc^2(\Bbb R)$ can be constructed,…
The first purpose of this paper is to show a method of constructing a regular biorthogonal pair based on the commutation rule: $ab-ba=I$ for a pair of operators $a$ and $b$ acting on a Hilbert space ${\cal H}$ with inner product $( \cdot |…
We obtain a criterion for the quasi-regularity of generalized (non-sectorial) Dirichlet forms, which extends the result of P.J. Fitzsimmons on the quasi-regularity of (sectorial) semi-Dirichlet forms. Given the right (Markov) process…
In \cite{b-i-t}, F. Bagarello, A. Inoue and C. Trapani investigated some operators defined by Riesz bases. These operators connect with ${\it quasi}$-${\it hermitian \; quantum \; mechanics}$, and its relatives. In this paper, we change the…
In the paper, we establish Gr\"obner-Shirshov bases for semirings and commutative semirings. As applications, we obtain Gr\"obner-Shirshov bases and A. Blass's (1995) and M. Fiore -T. Leinster's (2004) normal forms of the semirings…
In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new definition of fusion dual sequence associated with a fusion…
We prove that a semiregular topological space $X$ is completely regular if and only if its topology is generated by a normal quasi-uniformity. This characterization implies that each regular paratopological group is completely regular. This…
As a common non-trivial generalization of the concept of a proper generalized Bassian group, we introduce the notion of a semi-generalized Bassian group and initiate its comprehensive investigation. Precisely, we give a satisfactory…
In this paper we define and study quasipolar general rings (with or without identity) and extend many of the basic results to the wider class. We obtain some new characterizations of quasipolar and strongly $\pi$-regular elements by using…
We analyse special classes of biorthogonal sets of vectors in Hilbert and in Krein spaces, and their relations with $\mathcal{G}$- quasi bases. We also discuss their relevance in some concrete quantum mechanical system driven by manifestly…
Hitchin pairs on Riemann surfaces are generalizations of Higgs bundles, allowing the Higgs field to be twisted by an arbitrary line bundle. We consider this generalization in the context of $G$-Higgs bundles for a real reductive Lie group…
It is well known that a sequence in a Hilbert space is a Riesz basis if and only if it is a complete Bessel sequence with biorthogonal sequence which is also a complete Bessel sequence. Here we prove that the completeness of one (any one)…
A generalization of Mallat's classic theory of multiresolution analysis based on the theory of spectral pairs was considered by Gabardo and Nashed (J. Funct. Anal. 158, 209-241, 1998). In this article, we introduce the notion of…
The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow to deduce effortlessly general criteria for the geometric convergence of normalized unbounded semigroups.
The set of idempotents of a regular semigroup is given an abstract characterization as a regular biordered set in [2], and in [4] it is shown how a biordered set can be associated with a complemented modular lattice. Von Neumann has shown…
Distance-regular graphs are a class of regualr graphs with pretty combinatorial symmetry. In 2007, Miklavi\v{c} and Poto\v{c}nik proposed the problem of charaterizing distance-regular Cayley graphs, which can be viewed as a natural…
In a paper from 1996, D. Jerison and C. Kenig among other results provided a $H^{1/2}$ regularity result for the Dirichlet problem for the Laplace equation in Lipschitz domains. In this article, we adopt a Hilbertian approach to construct…