Related papers: Decomposable operators, local S-spectrum and S-spe…
We establish that the complete theory of a Hilbert space equipped with a normal operator has the Schr\"oder-Bernstein property. This answers a question of Argoty, Berenstein, and the first-named author. We also prove an analogous statement…
In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of $S$-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and…
Let $H_0$ be a purely absolutely continuous selfadjoint operator acting on some separable infinite-dimensional Hilbert space and $V$ be a compact non-selfadjoint perturbation. We relate the regularity properties of $V$ to various spectral…
In this paper we introduce fractional powers of quaternionic operators. Their definition is based on the theory of slice-hyperholomorphic functions and on the $S$-resolvent operators of the quaternionic functional calculus. The integral…
We introduce the spectral points of two-sided positive type of bounded normal operators in Krein spaces. It is shown that a normal operator has a local spectral function on sets which are of two-sided positive type. In addition, we prove…
Selfadjoint and maximal dissipative extensions of a non-densely defined symmetric operator $S$ in an infinite-dimensional separable Hilbert space are considered and their compressions on the subspace ${\rm \overline{dom}\,} S$ are studied.…
We continue a line of study about some local versions of Bishop-Phelps-Bollob\'as type properties for bounded linear operators. We introduce and focus our attention on two of these local properties, which we call L$_{p, o}$ and L$_{o, p}$,…
This paper extends the notion of a p-hyponormal operator for a bounded right linear quaternionic operator defined on a right quaternionic Hilbert space. Several fundamental properties of complex p-hyponormal operators are investigated for…
We study some local spectral properties of contraction operators on $\ell_p$, $1<p<\infty$ from a Baire category point of view, with respect to the Strong$^*$ Operator Topology. In particular, we show that a typical contraction on $\ell_p$…
We study the spectral properties of positive absolutely minimum attaining operators defined on infinite dimensional complex Hilbert spaces and using that derive a characterization theorem for such type of operators. We construct several…
The spectral theory on the $S$-spectrum was born out of the need to give quaternionic quantum mechanics (formulated by Birkhoff and von Neumann) a precise mathematical foundation. Then it turned out that this theory has important…
we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable…
Joint spectra of tuples of operators are subsets in complex projective space. The corresponding tuple of operators can be viewed as an infinite dimensional analog of a determinantal representation of the joint spectrum. We investigate the…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
In the present paper, we prove a resolvent equation for the $\mathcal{S}$-resolvent operator in the quaternionic framework. Exploiting this resolvent equation, we find a series expansion for the $\mathcal{S}$-resolvent operator in an open…
Results of Haagerup and Schultz (2009) about existence of invariant subspaces that decompose the Brown measure are extended to a large class of unbounded operators affiliated to a tracial von Neumann algebra. These subspaces are used to…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
Given a LHS (Lattice of Hilbert spaces) $V_J$ and a symmetric operator $A$ in $V_J$, in the sense of partial inner product spaces, we define a generalized resolvent for $A$ and study the corresponding spectral properties. In particular, we…
Given a densely defined and closed operator $A$ acting on a complex Hilbert space $\mathcal{H}$, we establish a one-to-one correspondence between its closed extensions and subspaces $\mathfrak{M}\subset\mathcal{D}(A^*)$, that are closed…