Let A be a Banach algebra. For f ∈ A*, we inspect the weak sequential properties of well-known map Tf : → (a) = fa, where fa A* is defined by fa(x) (ax) for all x A. We provide equivalent conditions when completely continuous every and maps weakly precompact sets onto L-sets A*. Our results have applications to algebra compact operators K(X) on space X.

This paper is devoted for the design and implementation of a 32bit Arithmetic module it is used for vedic Mathematics algorithms. We have various arithmetic multiplication techniques like Urdhva, Tiryakbhyam, Nikhilam, and Anurupye has been thoroughly analyzed. A 32 x 32 bit multiplier using Urdhava Tiryakbhyam, it has been designed and using this multiplier, a MAC unit has been designed. An Ar...

We study multiplication modules. The rings are not assumed to be commutative. Several criteria with some applications given for a direct sum of modules module.

The Hardy space H(D) can be viewed as a module over the polynomial ring C[z, w] with module action defined by multiplication of functions. The core operator is a bounded self-adjoint integral operator defined on submodules of H(D), and it gives rise to some interesting numerical invariants for the submodules. These invariants are difficult to compute or estimate in general. This paper computes ...

We introduce the concept of "uniformly primary submodules" of a module over a commutative ring R, which generalizes the concept of "uniformly primary ideals" of R, a concept that imposes a certain boundedness condition on the usual notion of "primary ideal". Several results on uniformly primary submodules are proved. Also, we characterize uniformly primary submodules of a multiplication module....

Module skew codes are one sidedmodules for (a quotient of) a skewpolynomial ringwhere multiplication is twisted by an automorphism of the Galois group of the alphabet field. We prove that long module skew codes over a fixed finite field are asymptotically good by using a non-constructive counting argument. We show that for fixed alphabet size, and automorphism order and large length their asymp...