Let H be a separable Hilbert space, and let D(B(H) ah) be the antiHermitian bounded diagonal operators in some fixed orthonormal basis and K(H) the compact operators. We study the group of unitary operators Uk,d = {u ∈ ...

Let M be a type II_1 von Neumann algebra,  τ a trace in M, and l^2 (M,τ) the GNS Hilbert space of τ. We regard the unitary group U_M as a subset of l^2 (M,τ), and characterize the shortest smooth curves of unitaries joining ...

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). ...

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 ...

A relationship between all the generalized Casimir operators of complementary unitary groups is derived, both in the fermion and boson realizations of the corresponding Lie algebras. It is shown that the number of independent ...

We study pairs (U, L) , where U is a unitary operator in H and L⊂ H is a closed subspace, such that PL0U|L0:L0→L0has a singular value decomposition. Abstract characterizations of this condition are given, as well as relations ...