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Monotonic solutions for quadratic integral equations

Mieczysław Cichoń, Mohamed M.A. Metwali (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Using the Darbo fixed point theorem associated with the measure of noncompactness, we establish the existence of monotonic integrable solution on a half-line ℝ₊ for a nonlinear quadratic functional integral equation.

Moore-Penrose inverses of Gram operators on Hilbert C*-modules

M. S. Moslehian, K. Sharif, M. Forough, M. Chakoshi (2012)

Studia Mathematica

Let t be a regular operator between Hilbert C*-modules and t † 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 t † = ( t * t ) † t * = t * ( t t * ) † and ( t * t ) † = t † t * † . As an application, we get some results for densely defined closed operators on Hilbert C*-modules over C*-algebras of compact operators.

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...

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 ∈ L p ( 0 , ∞ ) 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 ≤ 1 s u p f ∈ B p ʃ 0 ∞ 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 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.

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