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More classes of non-orbit-transitive operators

Carl Pearcy, Lidia Smith (2010)

Studia Mathematica

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...

More subnormal Toeplitz operators.

Carl C. Cowen (1986)

Journal für die reine und angewandte Mathematik

Morse-Sard theorem for real-analytic functions

Jiří Souček, Vladimír Souček (1972)

Commentationes Mathematicae Universitatis Carolinae

Morse-Sard theorem in infinite dimensional Banach spaces and investigation of the set of all critical levels

Svatopluk Fučík, Milan Kučera, Jindřich Nečas, Jiří Souček, Vladimír Souček (1974)

Časopis pro pěstování matematiky

Moser's Inequality for a class of integral operators

Finbarr Holland, David Walsh (1995)

Studia Mathematica

Let 1 < p < ∞, q = p/(p-1) and for $f \in L^{p} (0, \infty)$ define $F (x) = (1 / x) ʃ_{0}^{x} f (t) d t$ , x > 0. Moser’s Inequality states that there is a constant $C_{p}$ such that $s u p_{a \leq 1} s u p_{f \in B_{p}} ʃ_{0}^{\infty} e x p [a x^{q} {| F (x) |}^{q} - x] d x = C_{p}$ where $B_{p}$ is the unit ball of $L^{p}$ . Moreover, the value a = 1 is sharp. We observe that $F = K_{1}$ f where the integral operator $K_{1}$ 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...

Most Markov operators on C(X) are quasi-compact and uniquely ergodic

Ryszard Rębowski (1987)

Colloquium Mathematicae

Most random walks on nilpotent groups are mixing

R. Rębowski (1992)

Annales Polonici Mathematici

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.