Partial isometries in semi-Hilbertian spaces

By M. Arias, Gustavo Corach, M. C. Gonzalez. 2008

193 citations recorded by the source corpus.

In this work, the concepts of isometry, unitary and partial isometry on a Hilbert space are generalized when an additional semi-inner product is considered. These new concepts are described by means of oblique projections.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6b2add39593d3b9d57db0636d0988c17cf11da72

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Metric Properties of Projections in Semi-Hilbertian Spaces (2008, background): “In [2] we have studied some properties of the ] operation which are relevant for studying A-partial isometries, i.”
A note on the A-numerical radius of operators in semi-Hilbert spaces (2020, background): “For more results and proofs related to this class of operators, we invite the reader to consult [1,2] and their references.”
Ergodic properties of operators in some semi-Hilbertian spaces (2013, background): “The inspiration for our investigation comes from [1,2,11,12].”
Some improvements of numerical radius inequalities of operators and operator matrices (2019, unknown): “Formore informationwe refer the reader to [15, 18, 19].”
Joint normality of operators in semi-Hilbertian spaces (2020, methodology): “In the next proposition we collect some properties of T (for the proof see [5] and [7]).”
A-Numerical Radius Orthogonality and Parallelism of Semi-Hilbertian Space Operators and Their Applications (2020, background): “An operator U ∈ BA(H) is said to be A-unitary if ‖Ux‖A = ‖U A x‖A = ‖x‖A for all x ∈ H (see [2]).”
On inequalities for A-numerical radius of operators (2019, background): “For further details we refer the reader to [1, 2, 3].”
A-numerical radius inequalities for semi-Hilbertian space operators (2019, background): “For proofs and more facts about this class of operators, we refer the reader to [4, 5] and their references.”
Positivity of $2\times 2$ block matrices of operators (2019, background): “Such adjoint T has many properties similar to those of the usual adjoint T ∗; see [4].”