A class of Banach lattices and positive operators
We characterize the bounded linear operators T in Hilbert space which satisfy T = βI + (1-β)S where β ∈ (0,1) and S is a contraction. The characterizations include a quadratic form inequality, and a domination condition of the discrete semigroup by the continuous semigroup . Moreover, we give a stronger quadratic form inequality which ensures that . The results apply to large classes of Markov operators on countable spaces or on locally compact groups.
This article provided some sufficient or necessary conditions for a class of integral operators to be bounded on mixed norm spaces in the unit ball.
In [P] we characterize the pairs of weights for which the fractional integral operator of order from a weighted Lebesgue space into a suitable weighted and Lipschitz integral space is bounded. In this paper we consider other weighted Lipschitz integral spaces that contain those defined in [P], and we obtain results on pairs of weights related to the boundedness of acting from weighted Lebesgue spaces into these spaces. Also, we study the properties of those classes of weights and compare...
We study the existence of positive solutions to a class of singular nonlinear fourth-order boundary value problems in which the nonlinearity may lack homogeneity. By introducing suitable control functions and applying cone expansion and cone compression, we prove three existence theorems. Our main results improve the existence result in [Z. L. Wei, Appl. Math. Comput. 153 (2004), 865-884] where the nonlinearity has a certain homogeneity.
We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other inclusion is shown to hold when the constant sequences belong to the subshift generated by the given biinfinite sequence. Applying recent results by S. N....