Let S be a locally compact topological foundation semigroup with identity and Ma(S) be its semigroup algebra. In this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $M_a(S)$ of a locally compact topological foundationsemigroup with identity.

We survey the recent investigations on (bounded, sequential) approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We will discuss the core problems concerning these notions and address the signicance of any solutions to them to the development of the eld.

We investigate the stability of generalizedderivations on Banach algebras with a bounded central approximateidentity. We show that every approximate generalized derivation inthe sense of Rassias, is an exact generalized derivation. Also thestability problem of generalized derivations on the faithful Banachalgebras is investigated.

We prove that, for every extension of Banach algebras 0 → B → A → D → 0 such that B has a left or right bounded approximate identity, the existence of an associated long exact sequence of Banach simplicial or cyclic cohomology groups is equivalent to the existence of one for homology groups. It follows from the continuous version of a result of Wodzicki that associated long exact sequences exis...

In a recent paper, S.-E. Takahasi defined the notion of a BSE Banach module over a commutative Banach algebra A with bounded approximate identity. We show that the multiplier space &f(X) of X can be represented as a space of sections in a bundle of Banach spaces, and we use bundle techniques to obtain shorter proofs of various of Takahasi’s results on P-algebra modules and to answer several que...

If a function f is of bounded variation on TN (N ≥ 1) and {φn} is a positive approximate identity, we prove that the area of the graph of f ∗φn converges from below to the relaxed area of the graph of f . Moreover we give asymptotic estimates for the area of the graph of the square partial sums of multiple Fourier series of functions with suitable discontinuities.

Reflectivists consider reflective reasoning crucial for good judgment and action. Anti-reflectivists deny that reflection delivers what reflectivists seek. Alas, the evidence is mixed. So, does confer normative value or not? This paper argues a middle way: can value, but its ability to do this bound by factors such as we might call epistemic identity: an identity involves particular beliefs—for...