Let G denote a locally compact Hausdorff abelian group. Then a bounded linear operator T from L^2(G) into L^2(G) is a bounded multiplier operator if, under the Fourier transform on L^2(G ), for each function f in L^2(G), T(f) changes into a bounded function U times the Fourier transform of f. Then U is called the multiplier of T. An unbounded multiplier operator has a similar definition, but it...

Let A be a Banach algebra with the second dual A∗∗. If A has a bounded approximate identity (= BAI), then A∗∗ is unital if and only if A∗∗ has a weak∗ bounded approximate identity(= W ∗BAI). If A is Arens regular and A has a BAI, then A∗ factors on both sides. In this paper we introduce new concepts LW ∗W and RW ∗W property and we show that under certain conditions if A has LW ∗W and RW ∗W prop...

Inexact (Approximate) computing is an attractive paradigm for digital processing. Inexact computing is particularly interesting for computer arithmetic designs. This project deals with the analysis and design of two new approximate 4-2 compressors for utilization in a multiplier. These designs rely on different features of compression, such that imprecision in computation can make up for circui...

In this talk, we present a trust region method for solving equality constrained optimization problems, which is motivated by the famous augmented Lagrangian function. It is different from standard augmented Lagrangian methods where the augmented Lagrangian function is minimized at each iteration. This method, for fixed Lagrange multiplier and penalty parameters, tries to minimize an approximate...

We study the space of functions ϕ: IN → C such that there is a Hilbert space H, a power bounded operator T in B(H) and vectors ξ, η in H such that ϕ(n) = T n ξ, η. This implies that the matrix (ϕ(i + j)) i,j≥0 is a Schur multiplier of B(ℓ 2) or equivalently is in the space (ℓ 1 ∨ ⊗ ℓ 1) *. We show that the converse does not hold, which answers a question raised by Peller [Pe]. Our approach make...

In this paper, we give a short survey of results and problems concerning the notion of bounded weak approximate identities in Banach algebras. Also, we introduce a new version of approximate identities and give one illuminating example to show the difference.

We give a counterexample to a conjecture of S.E. Morris by showing that there is a compact plane set X such that R(X) has no non-zero, bounded point derivations but such that R(X) is not weakly amenable. We also give an example of a separable uniform algebra A such that every maximal ideal of A has a bounded approximate identity but such that A is not weakly amenable.

We consider in dimension four weakly convergent sequences of approximate biharmonic maps to a Riemannian manifold with bi-tension fields bounded in L for p > 4 3 . We prove an energy identity that accounts for the loss of hessian energies by the sum of hessian energies over finitely many nontrivial biharmonic maps on R. As a corollary, we obtain an energy identity for the heat flow of biharmoni...

The rule of an approximate identity is as follows: A function f which has to be approximated is convolved with a kernel Kδ for some δ. If the kernel satisfies certain conditions then the convolutions converge in a certain limit such as δ → 0+ to f . Note that approximate identities for scalar function on balls in R are studied e.g. in [14]. Further works on localizing kernels, like scaling func...

for any reduced commutative $f$-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. the condition is that every minimal ideal of the ring consist entirely of bounded elements. it is not too stringent, and is satisfied, for instance, by rings of conti...