Displaying similar documents to “On a problem of Nieminen”

Unitary dilation for polar decompositions of p-hyponormal operators

Muneo Chō, Tadasi Huruya, Kôtarô Tanahashi (2005)

Banach Center Publications

Similarity:

In this paper, we introduce the angular cutting and the generalized polar symbols of a p-hyponormal operator T in the case where U of the polar decomposition T = U|T| is not unitary and study spectral properties of it.

Diagonals of Self-adjoint Operators with Finite Spectrum

Marcin Bownik, John Jasper (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

Given a finite set X⊆ ℝ we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the Schur-Horn theorem from a finite-dimensional setting to an infinite-dimensional Hilbert space analogous to Kadison's theorem for orthogonal projections (2002) and the second author's result for operators with three-point spectrum (2013).

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

Mohammed Hichem Mortad (2011)

Colloquium Mathematicae

Similarity:

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.

On dilation and commuting liftings of n-tuples of commuting Hilbert space contractions

Zbigniew Burdak, Wiesław Grygierzec (2020)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Similarity:

The n-tuples of commuting Hilbert space contractions are considered. We give a model of a commuting lifting of one contraction and investigate conditions under which a commuting lifting theorem holds for an n-tuple. A series of such liftings leads to an isometric dilation of the n-tuple. The method is tested on some class of triples motivated by Parrotts example. It provides also a new proof of the fact that a positive definite n-tuple has an isometric dilation.