assume that $a$‎, ‎$b$ are banach algebras and that $m:atimes brightarrow b$‎, ‎$m^prime:atimes arightarrow b$ are bounded bilinear mappings‎. ‎we study the relationships between arens regularity of $m$‎, ‎$m^prime$ and the banach algebras $a$‎, ‎$b$‎. ‎for a banach $a‎$‎-bimodule $b$‎, ‎we show that $b$ factors with respect to $a$ if and only if $b^{**}$ is unital as an $a^{**}‎$‎-module‎. ‎le...

Commutators of a large class of bilinear operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be jointly compact. Under a similar commutation, fractional integral versions of the bilinear Hilbert transform yield separately compact operators.

In this paper, a method to design a bank of unknown input residual generator (UIRG) for fault detection and isolation is investigated. The plant model is assumed to be a bounded control inputs singular bilinear systems (SBS) subjected to unknown disturbances. The measurements can be bilinear.

In this paper we will prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators, that is, we prove the weighted Lp norm is bounded by the weighted Lp norm of a natural maximal operator when the weight belongs to A∞. As a corollary we are able to obtain new weighted esti...

A new instantiation of the Cramer-Shoup paradigm for secure encryption is presented, which is built using bilinear map groups. The security is based on the Bilinear Decisional Diffie-Hellman assumption. The recent efficiency improvements introduced in [KD04,GS04] are also applied to our constructions. One of the schemes thereby obtained presents efficiency similar to the most efficient encrypti...

Note that the three vector spaces involved aren’t necessarily the same. What these examples have in common is that in each case, the product is a bilinear map. The tensor product is just another example of a product like this. If V1 and V2 are any two vector spaces over a field F, the tensor product is a bilinear map: V1 × V2 → V1 ⊗ V2 , where V1 ⊗ V2 is a vector space over F. The tricky part i...

Alternating bilinear maps with few relations allow to define a combinatorial closure similarly as in [2]. For the א0-categorical case we show that this closure is part of the algebraic closure.

Let -----. For an analytic self-map ---  of --- , Let --- be the composition operator with composite map ---  so that ----. Let ---  be a bounded analytic function on --- . The weighted composition operator ---  is defined by --- . Suppose that ---  is the Hardy space, consisting of all analytic functions defined on --- , whose Maclaurin cofficients are square summable. .....

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.