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Elements of C*-algebras commuting with their Moore-Penrose inverse

J. Koliha (2000)

Studia Mathematica

We give new necessary and sufficient conditions for an element of a C*-algebra to commute with its Moore-Penrose inverse. We then study conditions which ensure that this property is preserved under multiplication. As a special case of our results we recover a recent theorem of Hartwig and Katz on EP matrices.

Equivalence of Decomposability and 2-Decomposability for Several Commuting Operators.

Jörg Eschmeier (1983)

Mathematische Annalen

Ergodic Families of Affine Operators.

J.J. Koliha, A.P. Leung (1975)

Mathematische Annalen

Estimates for absolute values of matrix functions.

Gil', Michael I. (2007)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Explicit solutions for boundary value problems related to the operator equations $X^{(2)} - A X = 0$

Lucas Jódar, Enrique A. Navarro (1991)

Applications of Mathematics

Cauchy problem, boundary value problems with a boundary value condition and Sturm-Liouville problems related to the operator differential equation $X^{(2)} - A X = 0$ are studied for the general case, even when the algebraic equation $X^{2} - A = 0$ is unsolvable. Explicit expressions for the solutions in terms of data problem are given and computable expressions of the solutions for the finite-dimensional case are made available.

Exponential bounds for noncommuting systems of matrices

Brian Jefferies (2001)

Studia Mathematica

It is shown that a finite system T of matrices whose real linear combinations have real spectrum satisfies a bound of the form $| | e^{i ⟨ T, ζ ⟩} | | \leq C (1 + {| ζ |)}^{s} e^{r | ℑ ζ |}$ . The proof appeals to the monogenic functional calculus.

Exponentials of bounded normal operators

Aicha Chaban, Mohammed Hichem Mortad (2013)

Colloquium Mathematicae

The present paper is mainly concerned with equations involving exponentials of bounded normal operators. Conditions implying commutativity of normal operators are given, without using the known 2πi-congruence-free hypothesis. This is a continuation of a recent work by the second author.

Exponentials of normal operators and commutativity of operators: a new approach

Mohammed Hichem Mortad (2011)

Colloquium Mathematicae

We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.

Extension of Analytic Functional Calculus Mappings and Duality by ...-Closed Forms with Growth.

Bernd Droste (1982)

Mathematische Annalen

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