Zero Jordan product determined Banach algebras

A Banach algebra $A$ is said to be a zero Jordan product determined Banach algebra if every continuous bilinear map $\varphi\colon A\times A\to X$, where $X$ is an arbitrary Banach space, which satisfies $\varphi(a,b)=0$ whenever $a$, $b\in A$ are such that $ab+ba=0$, is of the form $\varphi(a,b)=\sigma(ab+ba)$ for some continuous linear map $\sigma$. We show that all $C^*$-algebras and all group algebras $L^1(G)$ of amenable locally compact groups have this property, and also discuss some applications

Maps preserving zeros of a polynomial

Let \A be an algebra and let $f(x_1,...,x_d)$ be a multilinear polynomial in noncommuting indeterminates $x_i$. We consider the problem of describing linear maps \phi:\A\to \A that preserve zeros of $f$. Under certain technical restrictions we solve the problem for general polynomials $f$ in the case where \A=M_n(F). We also consider quite general algebras \A, but only for specific polynomials $f$.Comment: 11 pages, accepted for publication in Linear Algebra App

The Kadison problem on a class of commutative Banach algebras with closed cone

summary:The main result of the paper characterizes continuous local derivations on a class of commutative Banach algebra $A$ that all of its squares are positive and satisfying the following property: Every continuous bilinear map $\Phi$ from $A\times A$ into an arbitrary Banach space $B$ such that $\Phi(a,b)=0$ whenever $ab=0$, satisfies the condition $\Phi (ab,c)=\Phi(a,bc)$ for all $a,b,c\in A$

Effects of ultrasound treatments on wine microorganisms

Ultrasound is one of the most promising non-thermal an emerging technique in food technology. The objective of the present work was to evaluate the effect of different ultrasonic treatments on the most important wine microbiota (Saccharomyces and non-Saccharomyces yeasts and lactic acid bacteria). Two stages were carried out: the assessment step, where six different ultrasonic treatments (with varying power, time, and pulses) were used on Saccharomyces cerevisiae, Brettanomyces spp., and Lactiplantibacillus plantarum; and the validation step, where two chosen ultrasonic treatments were used on Zigosaccharomyces bailli, Brettanomyces spp., Saccharomyces cerevisiae, Saccharomyces bayanus, Pichia membranifaciens, Schizosaccharomyces pombe, and Hanseniaspora osmophila. The most sensitive microorganism was Brettanomyces spp., and the most resistant was Lactiplantibacillus plantarum. Ultrasonic treatments had varying effects on vitality (delay of growth or maximum OD reduction) and on viability (reduction of microbial growth)