Geodesic neighborhoods in unitary orbits of self-adjoint operators of K+C
نویسندگان
چکیده
In the present paper, we study unitary orbit of a compact Hermitian diagonal operator with spectral multiplicity one under action group U K + C unitization operators ( H ) , or equivalently, quotient / D . We relate this and different subgroups to describe metric geodesics (using natural distance) which join end points. As consequence obtain local Hopf-Rinow theorem. also explore cases about uniqueness short curves prove that there exist some these cannot be parameterized using minimal anti-Hermitian
منابع مشابه
Lecture Vi: Self-adjoint and Unitary Operators
De nition. Let (V, 〈 , 〉) be a n-dimensional euclidean vector space and T : V −→ V a linear operator. We will call the adjoint of T , the linear operator S : V −→ V such that: 〈T (u), v〉 = 〈u, S(v)〉 , for all u, v ∈ V . Proposition 1. Let (V, 〈 , 〉) be a n-dimensional euclidean vector space and T : V −→ V a linear operator. The adjoint of T exists and is unique. Moreover, if E denotes an orthon...
متن کاملThe Spectral Theorem for Self-Adjoint and Unitary Operators
(1.1) (Au, v) = (u, A∗v), u, v ∈ H. We say A is self-adjoint if A = A∗. We say U ∈ L(H) is unitary if U∗ = U−1. More generally, if H is another Hilbert space, we say Φ ∈ L(H,H) is unitary provided Φ is one-to-one and onto, and (Φu, Φv)H = (u, v)H , for all u, v ∈ H. If dim H = n < ∞, each self-adjoint A ∈ L(H) has the property that H has an orthonormal basis of eigenvectors of A. The same holds...
متن کاملDiagonals of Self-adjoint Operators
The eigenvalues of a self-adjoint n×n matrix A can be put into a decreasing sequence λ = (λ1, . . . , λn), with repetitions according to multiplicity, and the diagonal of A is a point of R that bears some relation to λ. The Schur-Horn theorem characterizes that relation in terms of a system of linear inequalities. We prove an extension of the latter result for positive trace-class operators on ...
متن کاملUnitary Orbits of Normal Operators in Von Neumann Algebras
The starting points for this paper are simple descriptions of the norm and strong* closures of the unitary orbit of a normal operator in a von Neumann algebra. The statements are in terms of spectral data and do not depend on the type or cardinality of the algebra. We relate this to several known results and derive some consequences, of which we list a few here. Exactly when the ambient von Neu...
متن کاملFunctions of self-adjoint operators in ideals of compact operators
For self-adjoint operators A,B, a bounded operator J , and a function f : R → C, we obtain bounds in quasi-normed ideals of compact operators for the difference f(A)J − Jf(B) in terms of the operator AJ − JB. The focus is on functions f that are smooth everywhere except for finitely many points. A typical example is the function f(t) = |t|γ with γ ∈ (0, 1). The obtained results are applied to d...
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: Differential Geometry and Its Applications
سال: 2021
ISSN: ['1872-6984', '0926-2245']
DOI: https://doi.org/10.1016/j.difgeo.2021.101778