English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We establish new estimates to compute the $\lambda$-function of Aron andLohman on the unit ball of a JB$^*$-triple. It is established that for everyBrown-Pedersen quasi-invertible element $a$ in a JB$^*$-triple $E$ we have$$\hbox{dist} (a, \mathfrak{E} (E_1)) = \max \left\{ 1- m_q (a) ,\|a\|-1\right\},$$ where $\mathfrak{E} (E_1)$ denotes the set of extreme pointsof the closed unit ball $E_1$ of $E$. It is proved that $\lambda (a) =\frac{1+m_q (a)}{2},$ for every Brown-Pedersen quasi-invertible element $a$ in$E_1$, where $m_q (a)$ is the square root of the quadratic conorm of $a$. Foran element $a$ in $E_1$ which is not Brown-Pedersen quasi-invertible we canonly estimate that $\lambda (a)\leq \frac12 (1-\alpha_q (a)).$ A completedescription of the $\lambda$-function on the closed unit ball of everyJBW$^*$-triple is also provided, and as a consequence, we prove that everyJBW$^*$-triple satisfies the uniform $\lambda$-property.

Approximation and convex decomposition by extremals and the $\lambda$-function in JBW*-triples