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Minimal length curves in unitary orbits of a Hermitian compact operator
(Elsevier Science, 2016-04)
We study some examples of minimal length curves in homogeneous spaces of B(H) under a left action of a unitary group. Recent results relate these curves with the existence of minimal (with respect to a quotient norm) ...
Geometry of the projective unitary group of a C*-algebra
(Unión Matemática Argentina, 2017-06)
Let A be a C∗-algebra with a faithful state ϕ. It is proved thatthe projective unitary group P UA of A,P UA = UA/T.1,(UA denotes the unitary group of A) is a C∞-submanifold of the Banach spaceBs(A) of bounded operators ...
The rectifiable distance in the unitary Fredholm group
(Polish Academy of Sciences. Institute of Mathematics, 2010-02)
Let Uc(H)={u:u unitary and u−1 compact} stand for the unitary Fredholm group. We prove the following convexity result. Denote by d∞ the rectifiable distance induced by the Finsler metric given by the operator norm in Uc(H). ...
Geometry of unitaries in a finite algebra: variation formulas and convexity
(World Scientific, 2008-12)
Given a C∗-algebra A with trace τ, we compute the first and second variation formulas for the p-energy functional Fp of the unitary group UA of A, for p = 2n an even integer, namely: Fp(γ) = Z b a τ([ ˙γ∗γ˙ ] n)dt, where ...
Thompson-type formulae
(2012)
On the discrete Wigner function for SU(N)
(Iop Publishing Ltd, 2019-10-04)
We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and generators of the special ...
Abstract Dispersive Estimates for Unitary Operators
(2018)
Let U be a unitary operator defined on a separable infinite-dimensional complex Hilbert space
H. Under suitable positivity and regularity assumptions, expressed in terms of higher order commutators,
we prove the existence ...
Non-unitary evolution of quantum logics
(Springer Science and Business Media, LLC, 2016-05)
In this work we present a dynamical approach to quantum logics. By changing the standard formalism of quantum mechanics to allow non-Hermitian operators as generators of time evolution, we address the question of how can ...