Polar decomposition of the Aluthge transformation in Hilbert C*-modules

Mahnaz Chakoshi

doi:10.2298/pim1818281c

Polar decomposition of the Aluthge transformation in Hilbert C*-modules

Publications de l Institut Mathematique ◽

10.2298/pim1818281c ◽

2018 ◽

Vol 104 (118) ◽

pp. 281-288

Author(s):

Mahnaz Chakoshi

Keyword(s):

Polar Decomposition ◽

Aluthge Transformation

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Polar decomposition and characterization of binormal operators

Filomat ◽

10.2298/fil2003013m ◽

2020 ◽

Vol 34 (3) ◽

pp. 1013-1024

Author(s):

Mehdi Mohammadzadeh Karizaki

Keyword(s):

Polar Decomposition ◽

Matrix Representation ◽

General Setting ◽

Inner Product ◽

Closed Range ◽

Aluthge Transformation ◽

The Matrix ◽

Closed Range Operator ◽

Equivalent Conditions

We illustrate the matrix representation of the closed range operator that enables us to determine the polar decomposition with respect to the orthogonal complemented submodules. This result proves that the reverse order law for the Moore-Penrose inverse of operators holds. Also, it is given some new characterizations of the binormal operators via the generalized Aluthge transformation. New characterizations of the binormal operators enable us to obtain equivalent conditions when the inner product of the binormal operator with its generalized Aluthge transformation is positive in the general setting of adjointable operators on Hilbert C*-modules.

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Polar Decomposition of Wiener Measure and Schwarzian Integrals

Lobachevskii Journal of Mathematics ◽

10.1134/s1995080220040228 ◽

2020 ◽

Vol 41 (4) ◽

pp. 709-713

Author(s):

E. T. Shavgulidze ◽

N. E. Shavgulidze

Keyword(s):

Polar Decomposition ◽

Wiener Measure

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Unbounded Wiener–Hopf Operators and Isomorphic Singular Integral Operators

Complex Analysis and Operator Theory ◽

10.1007/s11785-021-01110-w ◽

2021 ◽

Vol 15 (3) ◽

Author(s):

Domenico P. L. Castrigiano

Keyword(s):

Singular Integral ◽

Polar Decomposition ◽

Integral Operators ◽

Canonical Representation ◽

Friedrichs Extension ◽

Finite Dimensional ◽

Transformation Type ◽

Rational Symbols ◽

Shift Invariance ◽

Densely Defined

AbstractSome basics of a theory of unbounded Wiener–Hopf operators (WH) are developed. The alternative is shown that the domain of a WH is either zero or dense. The symbols for non-trivial WH are determined explicitly by an integrability property. WH are characterized by shift invariance. We study in detail WH with rational symbols showing that they are densely defined, closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains, ranges, spectral and Fredholm points are explicitly determined. Another topic concerns semibounded WH. There is a canonical representation of a semibounded WH using a product of a closable operator and its adjoint. The Friedrichs extension is obtained replacing the operator by its closure. The polar decomposition gives rise to a Hilbert space isomorphism relating a semibounded WH to a singular integral operator of Hilbert transformation type. This remarkable relationship, which allows to transfer results and methods reciprocally, is new also in the thoroughly studied case of bounded WH.

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