Operators preserving sesquilinear form
نویسندگان
چکیده
منابع مشابه
A 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 کاملPositive Sesquilinear Form Measures and Generalized Eigenvalue Expansions
Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized eigenvalue type expansions. Though there are formal similarities with earlier approaches to special cases of the problem, the paper differs e.g. from standar...
متن کاملDiagonalization and Representation Results for Nonpositive Sesquilinear Form Measures
We study decompositions of operator measures and more general sesquilinear form measures E into linear combinations of positive parts, and their diagonal vector expansions. The underlying philosophy is to represent E as a trace class valued measure of bounded variation on a new Hilbert space related to E. The choice of the auxiliary Hilbert space fixes a unique decomposition with certain proper...
متن کاملNonvanishing of a Certain Sesquilinear Form in the Theta Correspondence
Suppose 2n + 1 ≥ p + q. In an earlier paper in 2000 we study a certain sesquilinear form (, )π introduced by Jian-Shu Li in 1989. For π in the semistable range of θ(MO(p, q) → MSp2n(R)), if (, )π does not vanish, then it induces a sesquilinear form on θ(π). In another work in 2000 we proved that (, )π is positive semidefinite under a mild growth condition on the matrix coefficients of π. In thi...
متن کاملUnitary Operators Preserving Wavelets
We characterize a special class of unitary operators that preserve orthonormal wavelets. In the process we also prove that symmetric wavelet sets cover the real line.
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: 2015
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.12.008