In this paper Lambert multipliers acting between $L^p$ spaces are characterized by using some properties of conditional expectation operator. Also, Fredholmness of corresponding bounded operators is investigated.
Description of multiplication operators generated by a sequence and composition operators induced by a partition on Lorentz sequence spaces l(p, q), 1 < p ≤ ∞, 1 ≤ q ≤ ∞ is presented.
This paper deals with the generalized nonlinear third-order left focal problem at resonance (p(t)u ′′(t))′ − q(t)u(t) = f(t, u(t), u′ (t), u′′(t)), t ∈ ]t0, T[, m(u(t0), u′′(t0)) = 0, n(u(T), u′ (T)) = 0, l(u(ξ), u′ (ξ), u′′(ξ)) = 0, where the nonlinear term is a Carathéodory function and contains explicitly the first and second-order derivatives of the unknown function. The boundary conditions that we study are quite general, involve a linearity and include, as particular cases, Sturm-Liouville boundary conditions. Under certain growth conditions on the nonlinearity, we establish the existence of the nontrivial solutions by using the topological degree technique as well as some recent generalizations of this technique. Our results are generalizations and extensions of the results of several authors. An application is included to illustrate the results obtained.
First, some classic properties of a weighted Frobenius-Perron operator P u ϕ on L 1 (Σ) as a predual of weighted Koopman operator W = uUϕ on L∞(Σ) will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of P u ϕ under certain conditions