Related papers: Weighted projections into closed subspaces
In this paper we study the Weihrauch complexity of projection operators onto closed subsets of the Euclidean space. We show that some fundamental degrees of the Weihrauch lattice can be characterized in terms of such operators.
We develope new lower bounds for the $A$-numerical radius of semi-Hilbertian space operators, and applying these bounds we obtain upper bounds for the $A$-numerical radius of the commutators of operators. The bounds obtained here improve on…
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral…
We consider a variant of the notion of Morita equivalence appropriate to weak* closed algebras of Hilbert space operators, which we call {\em weak Morita equivalence}. We obtain new variants, appropriate to the dual algebra setting, of the…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of…
Extending the notion of parallelism we introduce the concept of approximate parallelism in normed spaces and then substantially restrict ourselves to the setting of Hilbert space operators endowed with the operator norm. We present several…
This paper introduces and investigates the class of \textit{$k$-quasi $n$-power posinormal operators} in Hilbert spaces, generalizing both posinormal and $n$-power posinormal operators. We establish fundamental properties including matrix…
We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…
We investigate algebraicity properties of quotients of complex spaces by complex reductive Lie groups G. We obtain a projectivity result for compact momentum map quotients of algebraic G-varieties. Furthermore, we prove equivariant versions…
We begin a program of generalizing basic elements of the theory of comparison, equivalence, and subequivalence, of elements in C*-algebras, to the setting of more general algebras. In particular, we follow the recent lead of Lin, Ortega,…
We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm…
This work is devoted to establish the strong convergence results of an iterative algorithm generated by the shrinking projection method in Hilbert spaces. The proposed approximation sequence is used to find a common element in the set of…
Let T be a quasidiagonal operator on a separable Hilbert space. Then T is the norm limit of operators, each of which generate a finite dimensional C*-algebra, if and only if the C*-algebra generated by T is exact.
Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the…
Motivated by two norm equations used to characterize the Friedrichs angle, this paper studies $C^*$-isomorphisms associated with two projections by introducing the matched triple and the semi-harmonious pair of projections. A triple…
Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…
In this paper, we study the operator equation $AB=\lambda BA$ for a bounded operator $A,B$ on a complex Hilbert space. We focus on algebraic relations between different operators that include normal, $M$-hyponormal, quasi $*$-paranormal and…
New inequalities for the $A$-numerical radius of the products and sums of operators acting on a semi-Hilbert space, i.e. a space generated by a positive semidefinite operator $A$, are established. In particular, it is proved for operators…