let x be a banach space of dimx > 2 and b(x) be the space of bounded linear operators on x. if l : b(x) → b(x) be a lie higher derivation on b(x), then there exists an additive higher derivation d and a linear map τ : b(x) → fi vanishing at commutators [a, b] for all a, b ∈ b(x) such that l = d + τ

In this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. Thena relation between totally fuzzy bounded sets and N-compactness is discussed.Finally, a geometric characterization for fuzzy totally bounded sets in I- topologicalvector spaces is derived.

There do not exist context–free languages of intermediate growth. The function γ whose value at each non–negative integer n is the number of words on length n in a fixed formal language L is called the growth function of L. Flajolet [3] asked if there are context–free languages of intermediate growth; that is, such that γ is not bounded above by a polynomial, but lim sup γ(n)/r = 0 for all r > ...

for some fixed large N0; we shall call such weights admissible. Rubio de Francia [11] showed that for every w ∈ L(R) there is a nonnegative W ∈ L(R) such that ‖W‖2 ≤ Cλ‖w‖2, Cλ < ∞ if λ > 0, and the analogous weighted norm inequality for S t holds uniformly in t. He used methods related to factorization theory of operators and the proof gave no information on how to construct w from W . In [3] ...

Let L be the space of complex-valued functions f on the set of vertices T of an infinite tree rooted at o such that the difference of the values of f at neighboring vertices remains bounded throughout the tree, and let Lw be the set of functions f ∈ L such that |f v − f v− | O |v|−1 , where |v| is the distance between o and v and v− is the neighbor of v closest to o. In this paper, we character...

In this paper two-dimensional Vilenkin-like systems will be investigated. We prove the Sunouchi operator is bounded from H to L for (2/3 < q ≤ 1). As a consequence, we prove the Sunouchi operator is L bounded for 1 < s < ∞ and of weak type (H, L).

Let L : C∞(M ;E)→ C∞(M ;E) be a second order, uniformly elliptic, semipositive-definite differential operator on a complete Riemannian manifold of bounded geometry M , acting between sections of a vector bundle with bounded geometry E over M . We assume that the coefficients of L are uniformly bounded. Using finite speed of propagation for L, we investigate properties of operators of the form f...

Many problems in the verification of concurrent software systems reduce to checking the non-emptiness of the intersection of contextfree languages, an undecidable problem. We propose a decidable underapproximation, and a semi-algorithm based on the under-approximation, for this problem through bounded languages. Bounded languages are context-free subsets of regular languages of the form w∗ 1w ∗...

Let  $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such  as Segal algebras and $L^1$-algebras are resp...

Suppose a sequence of random variables fX n g has negative drift when above a certain threshold and has increments bounded in L p. When p > 2 this implies that EX n is bounded above by a constant independent of n and the particular sequence fX n g. When p 2 there are counterexamples showing this does not hold. In general, increments bounded in L p lead to a uniform L r bound on X + n for any r ...