In this paper, using the Steklov function, we introduce the generalized continuity modulus and denethe class of functions Wr;kp;' in the space Lp. For this class, we prove an analog of the estimates in [1]in the space Lp.

We show that, if E is a Banach space with a basis satisfying a certain condition, then the Banach algebra l∞(K(l2 ⊕ E)) is not amenable; in particular, this is true for E = l with p ∈ (1,∞). As a consequence, l∞(K(E)) is not amenable for any infinite-dimensional Lp-space. This, in turn, entails the non-amenability of B(lp(E)) for any Lp-space E, so that, in particular, B(lp) and B(Lp[0, 1]) are...

In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.

We show that, if E is a Banach space with a shrinking basis satisfying a certain condition, then the Banach algebra l∞(K(l2⊕E)) is not amenable; in particular, this is true for E = l with p ∈ (1,∞). As a consequence, l∞(K(E)) is not amenable for any infinite-dimensional Lp-space. This, in turn, entails the non-amenability of B(lp(E)) for any Lp-space E, so that, in particular, B(lp) and B(Lp[0,...

The aim of this paper is to define an $L^p$ space intuitionistic fuzzy observables. We work in $({\mathcal F}, {\bf m})$ with product, where $\mathcal F$ a family events and ${\bf m}$ state. prove that the corresponding pseudometric $\rho_{IF}$ space.

Let G be the real line R, space R, the negative half-line R− or the octant R− := {(x1, · · · , xm) ∈ R : x1 ≤ 0, · · · , xm ≤ 0}. Let Lp = Lp(G), 1 ≤ p ≤ ∞, be the space of functions x : G → R, integrable in the power p on G (essentially bounded when p =∞), with usual norm. In the case when G = R or G = R−, by Lp = Lp(G), r ∈ N, we will denote the space of functions x : G → R, that have locally...

in this paper, we determine the structure of the space of multipliers of the range of a composition operator cφ that induces by the conditional expectation between two lp() spaces.

In 1969 Lindenstrauss and Rosenthal showed that if a Banach space is isomorphic to a complemented subspace of an Lp-space, then it is either a Lp-space or isomorphic to a Hilbert space. This is the motivation of this paper where we study non–Hilbertian complemented operator subspaces of non commutative Lp-spaces and show that this class is much richer than in the commutative case. We investigat...