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Search: MSC category 47B47 ( Commutators, derivations, elementary operators, etc. )

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1. CJM 2013 (vol 65 pp. 783)

Garcés, Jorge J.; Peralta, Antonio M.
Generalised Triple Homomorphisms and Derivations
We introduce generalised triple homomorphism between Jordan Banach triple systems as a concept which extends the notion of generalised homomorphism between Banach algebras given by K. Jarosz and B.E. Johnson in 1985 and 1987, respectively. We prove that every generalised triple homomorphism between JB$^*$-triples is automatically continuous. When particularised to C$^*$-algebras, we rediscover one of the main theorems established by B.E. Johnson. We shall also consider generalised triple derivations from a Jordan Banach triple $E$ into a Jordan Banach triple $E$-module, proving that every generalised triple derivation from a JB$^*$-triple $E$ into itself or into $E^*$ is automatically continuous.

Keywords:generalised homomorphism, generalised triple homomorphism, generalised triple derivation, Banach algebra, Jordan Banach triple, C$^*$-algebra, JB$^*$-triple
Categories:46L05, 46L70, 47B48, 17C65, 46K70, 46L40, 47B47, 47B49

2. CJM 2009 (vol 61 pp. 190)

Lu, Yufeng; Shang, Shuxia
Bounded Hankel Products on the Bergman Space of the Polydisk
We consider the problem of determining for which square integrable functions $f$ and $g$ on the polydisk the densely defined Hankel product $H_{f}H_g^\ast$ is bounded on the Bergman space of the polydisk. Furthermore, we obtain similar results for the mixed Haplitz products $H_{g}T_{\bar{f}}$ and $T_{f}H_{g}^{*}$, where $f$ and $g$ are square integrable on the polydisk and $f$ is analytic.

Keywords:Toeplitz operator, Hankel operator, Haplitz products, Bergman space, polydisk
Categories:47B35, 47B47

3. CJM 2005 (vol 57 pp. 1249)

Lindström, Mikael; Saksman, Eero; Tylli, Hans-Olav
Strictly Singular and Cosingular Multiplications
Let $L(X)$ be the space of bounded linear operators on the Banach space $X$. We study the strict singularity andcosingularity of the two-sided multiplication operators $S \mapsto ASB$ on $L(X)$, where $A,B \in L(X)$ are fixed bounded operators and $X$ is a classical Banach space. Let $1
Categories:47B47, 46B28

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