Surjective isometries on Grassmann spaces

DOI10.1016/j.jfa.2013.07.017zbMath1301.47100OpenAlexW2064314851MaRDI QIDQ2437032

Lajos Molnár, James E. Jamison, Maria Fernanda Botelho

Publication date: 28 February 2014

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2013.07.017

zbMATH Keywords

surjective isometryHilbert space projectionGrassmann spacegap metric

Mathematics Subject Classification ID

Abstract operator algebras on Hilbert spaces (47L30) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Related Items

Busch-Gudder metric on the cone of positive semidefinite operators and its isometries ⋮ Isometries of Grassmann spaces. II ⋮ An interpolation property of reflections involving orthogonal projections ⋮ General explicit descriptions for intertwining operators and direct rotations of two orthogonal projections ⋮ Wigner's theorem on Grassmann spaces ⋮ Ortho-isomorphisms of Grassmann spaces in semifinite factors ⋮ Surjective \(L^p\)-isometries on Grassmann spaces ⋮ Order type Tingley's problem for type \(I\) finite von Neumann algebras ⋮ Isometries of Grassmann spaces ⋮ Wigner-type theorem on transition probability preserving maps in semifinite factors ⋮ Isometries of the spaces of self-adjoint traceless operators ⋮ Isometries between projection lattices of von Neumann algebras ⋮ An elementary proof for the non-bijective version of Wigner's theorem ⋮ Analytic bundle structure on the idempotent manifold ⋮ Transition probability preserving maps on a Grassmann space in a semifinite factor ⋮ Commutativity preserving transformations on conjugacy classes of finite rank self-adjoint operators

Cites Work

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• Selected preserver problems on algebraic structures of linear operators and on function spaces
• Orthogonality preserving transformations on the set of \(n\)-dimensional subspaces of a Hilbert space
• Isometries and maps compatible with inverted Jordan triple products on groups
• Jordan's principal angles in complex vector spaces
• A Proof of the Mazur-Ulam Theorem
• Encyclopedia of Distances

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