We construct a Banach space Z such that the lattice of closed two-sided ideals of the Banach algebra B(Z) of bounded operators on Z is as follows: {0} ⊂ K (Z) ⊂ E (Z) ⊂ ⊂ M1 M2 ⊂ ⊂ We then determine which kinds of approximate identities (bounded/left/right), if any, each of the four non-trivial closed ideals of B(Z) contains, and we show that the maximal ideal M1 is generated as a left ideal by...

We prove that the multiplier algebra of the Drury-Arveson Hardy space H n on the unit ball in C n has no corona in its maximal ideal space, thus generalizing the famous Corona Theorem of L. Carleson in the unit disk. This result is obtained as a corollary of the Toeplitz Corona Theorem and a new Banach space result: the Besov-Sobolev space B p has the ”baby corona property” for all 0 ≤ σ < n p ...

By first describing the fixed maximal ideals of RL and those of its bounded part, R∗L, we show that every fixed maximal ideal of the bigger ring contracts to a fixed maximal ideal of the smaller ring, and every fixed maximal ideal of the smaller ring extends to a fixed maximal ideal of the bigger ring. However, the only instance where every maximal ideal of R∗L extends to a maximal ideal of RL ...

the aim of this paper is to introduce and study set- valued homomorphism on lattices and t-rough lattice with respect to a sublattice. this paper deals with t-rough set approach on the lattice theory. the result of this study contributes to, t-rough fuzzy set and approximation theory and proved in several papers. keywords: approximation space; lattice; prime ideal; rough ideal; t-rough set; set...

In [1] a recursive warrant semantics for Defeasible Logic Programming extended with levels of possibilistic uncertainty for defeasible rules was introduced. The resulting argumentation framework, called RP-DeLP, is based on a general notion of collective (non-binary) conflict among arguments allowing to ensure direct and indirect consistency properties with respect to the strict knowledge. An o...