Orthogonality preserving transformations of Hilbert Grassmannians
نویسندگان
چکیده
منابع مشابه
ORTHOGONALITY PRESERVING TRANSFORMATIONS ON THE SET OF n-DIMENSIONAL SUBSPACES OF A HILBERT SPACE
We characterize bijective transformations on the set of all n-dimensional subspaces of a Hilbert space that preserve orthogonality in both directions. This extends Uhlhorn’s improvement of Wigner’s classical theorem on symmetry transformations.
متن کاملA characterization of orthogonality preserving operators
In this paper, we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$. We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator. Also, we prove that every compact normal operator is a strongly orthogo...
متن کاملOrder Preserving Transformations of the Hilbert Grassmannian: Complex Case
Let H be a separable complex Hilbert space. Denote by G∞(H) the Grassmannian consisting of closed linear subspaces with infinite dimension and codimension. This Grassmannian is partially ordered by the inclusion relation. We show that every continuous order preserving bijective transformation of G∞(H) is induced by an invertible bounded semi-linear operator.
متن کاملNorm Preserving Extensions of Linear Transformations on Hilbert Spaces
Introduction. Let 77 be a Hubert space and let D be a closed proper subspace of 77. Let 70 be a linear contraction on D to 77. The problem of characterizing the contractions on all of 77 which extend J0 is directly related to the extension problems for unbounded transformations posed and treated by M. G. Krein [2] and R. S. Phillips [3]. In §1 of this paper we establish the following solution o...
متن کاملOrthogonal Apartments in Hilbert Grassmannians
Let H be an infinite-dimensional complex Hilbert space and let L(H) be the logic formed by all closed subspaces of H. For every natural k we denote by Gk(H) the Grassmannian consisting of k-dimensional subspaces. An orthogonal apartment of Gk(H) is the set consisting of all k-dimensional subspaces spanned by subsets of a certain orthogonal base of H. Orthogonal apartments can be characterized a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2020
ISSN: 0024-3795
DOI: 10.1016/j.laa.2020.07.019