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Numerical radius inequalities for Hilbert C * -modules

Sadaf Fakri Moghaddam, Alireza Kamel Mirmostafaee (2022)

Mathematica Bohemica

We present a new method for studying the numerical radius of bounded operators on Hilbert C * -modules. Our method enables us to obtain some new results and generalize some known theorems for bounded operators on Hilbert spaces to bounded adjointable operators on Hilbert C * -module spaces.

Nuovi risultati sulla semicontinuità inferiore di certi funzionali integrali

Luigi Ambrosio (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Given an open subset Ω of n and a Borel function f : Ω × × n [ 0 , + [ , conditions on f are given which assure the lower semicontinuity of the functional Ω f ( x , u , D u ) d x with respect to different topologies.

Obata’s Rigidity Theorem for Metric Measure Spaces

Christian Ketterer (2015)

Analysis and Geometry in Metric Spaces

We prove Obata’s rigidity theorem for metric measure spaces that satisfy a Riemannian curvaturedimension condition. Additionally,we show that a lower bound K for the generalizedHessian of a sufficiently regular function u holds if and only if u is K-convex. A corollary is also a rigidity result for higher order eigenvalues.

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