Let t be a regular operator between Hilbert C*-modules and be its Moore-Penrose inverse. We investigate the Moore-Penrose invertibility of the Gram operator t*t. More precisely, we study some conditions ensuring that and . As an application, we get some results for densely defined closed operators on Hilbert C*-modules over C*-algebras of compact operators.
In [JKP] and its sequel [FPS] the authors initiated a program whose (announced) goal is to eventually show that no operator in ℒ(ℋ) is orbit-transitive. In [JKP] it is shown, for example, that if T ∈ ℒ(ℋ) and the essential (Calkin) norm of T is equal to its essential spectral radius, then no compact perturbation of T is orbit-transitive, and in [FPS] this result is extended to say that no element of this same class of operators is weakly orbit-transitive. In the present note we show that no compact...
Let 1 < p < ∞, q = p/(p-1) and for define , x > 0. Moser’s Inequality states that there is a constant such that where is the unit ball of . Moreover, the value a = 1 is sharp. We observe that f where the integral operator has a simple kernel K. We consider the question of for what kernels K(t,x), 0 ≤ t, x < ∞, this result can be extended, and proceed to discuss this when K is non-negative and homogeneous of degree -1. A sufficient condition on K is found for the analogue...
Let G be a second countable locally compact nilpotent group. It is shown that for every norm completely mixing (n.c.m.) random walk μ, αμ + (1-α)ν is n.c.m. for 0 < α ≤ 1, ν ∈ P(G). In particular, a generic stochastic convolution operator on G is n.c.m.