Related papers: On some problems related to the Hilbert-Smith conj…
In infinite-dimensional Hilbert spaces, the application of the concept of quasi-Hermiticity to the description of non-Hermitian Hamiltonians with real spectra may lead to problems related to the definition of the metric operator. We discuss…
We study the computational complexity of satisfiability problems for classes of simple finite height (ortho)complemented modular lattices $L$. For single finite $L$, these problems are shown tobe $\mc{NP}$-complete; for $L$ of height at…
We establish the second part of Milnor's conjecture on the volume of simplexes in hyperbolic and spherical spaces. A characterization of the closure of the space of the angle Gram matrices of simplexes is also obtained.
We improve the Hyers-Ulam stability result for isometries of real Hilbert spaces by removing the surjectivity assumption.
We prove a Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations, which improves a classical result by Crandall and Rabinowitz in the case where basic spaces are Hilbert spaces. Actually, our theorem does not need any…
We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.
Given a locally convex vector space with a topology induced by Hilbert seminorms and a continuous bilinear form on it we construct a topology on its symmetric algebra such that the usual star product of exponential type becomes continuous.…
We provide a sufficient condition for a finite number of closed subspaces of a Hilbert space to be linearly independent and their sum to be closed. Under this condition a formula for the orthogonal projection onto the sum is given. We also…
This is a brief survey of some recent developments in the study of infinite dimensional Hopf algebras which are either noetherian or have finite Gelfand-Kirillov dimension. A number of open questions are listed.
We show that discretization of spacetime naturally suggests discretization of Hilbert space itself. Specifically, in a universe with a minimal length (for example, due to quantum gravity), no experiment can exclude the possibility that…
We review the notion of reducibility and we introduce and discuss the notion of orbital reducibility for autonomous ordinary differential equations of first order. The relation between (orbital) reducibility and (orbital) symmetry is…
We prove that a bounded linear Hilbert space operator has the unit circle in its essential approximate point spectrum if and only if it admits an orbit satisfying certain orthogonality and almost-orthogonality relations. This result is…
The article is devoted to the problem of Hilbert-Schmidt type analytic extensions in Hardy spaces over the infinite-dimensional unitary matrix group endowed with an invariant probability measure. An orthogonal basis of Hilbert-Schmidt…
These notes collect results about algebraic correspondences and adapt them to the setting of correspondences on projective lines. The focus lies on finite orbits of algebraic correspondences. The main result is a field theoretic…
In this paper, we study the Hilbert$-$Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how…
We give necessary and sufficient conditions for the sum of n subspaces of a Hilbert space to be closed. We also present various properties of n-tuples of subspaces with closed sum.
We present a purely algebraic formulation (i.e. polynomial equations only) of the minimum-cost multi-impulse orbit transfer problem without time constraints, while keeping all the variables with a precise physical meaning. We apply general…
In this expository note, we give a self-contained introduction to some modern incarnations of Hamiltonian reduction. Particular emphasis is placed on applications to symplectic geometry and geometric representation theory. We thereby…
We investigate Whitehead's asphericity question from a new perspective, using results and techniques of the homotopy theory of finite topological spaces. We also introduce a method of reduction to investigate asphericity based on the…