相关论文: Unbounded normal operators in octonion Hilbert spa…
Families of quasi-permutable normal operators in octonion Hilbert spaces are investigated. Their spectra are studied. Multiparameter semigroups of such operators are considered. A non-associative analog of Stone's theorem is proved.
A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special…
We study the numerical range of bounded linear operators on quaternionic Hilbert spaces and its relation with the S-spectrum. The class of complex operators on quaternionic Hilbert spaces is introduced and the upper bild of normal complex…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral…
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
General, especially spectral, features of compact normal operators in quaternionic Hilbert spaces are studied and some results are established which generalize well-known properties of compact normal operators in complex Hilbert spaces.…
We study some basic properties of the class of universal operators on Hilbert space, and provide new examples of universal operators and universal pairs.
In this article, we prove the following spectral theorem for right linear normal operators (need not to be bounded) in quaternionic Hilbert spaces: Let $T$ be an unbounded right quaternionic linear normal operator in a quaternionic Hilbert…
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
This paper delves into several characterizations of $A$-approximate point spectrum of A-bounded operators acting on a complex semi-Hilbertian space $H$ and also investigates properties of the $A$-approximate point spectrum for the tensor…
The paper introduces unbounded antilinear operators on Hilbert spaces and develops their fundamental theory. In particular, we establish a closed range theorem, a polar decomposition theorem, and the convexity of the numerical range for…
In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm in the unit sphere. We prove important results concerning the characterization of the AN operators, see Definition 1.2. The class of AN…
The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…
We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately.…
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…
Unbounded composition operators in $L^2$-space over discrete measure spaces are investigated. Normal, formally normal and quasinormal composition operators acting in $L^2$-spaces of this kind are characterized.
Motivated by potential theory on discrete spaces, we study a family of unbounded Hermitian operators in Hilbert space which generalize the usual graph-theoretic discrete Laplacian. These operators are discrete analogues of the classical…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
We study the spectral properties of bounded and unbounded Jacobi matrices whose entries are bounded operators on a complex Hilbert space. In particular, we formulate conditions assuring that the spectrum of the studied operators is…