#### Location

Cupples I Room 218

#### Start Date

7-18-2016 3:30 PM

#### End Date

18-7-2016 3:50 PM

#### Description

The open ball centered at an invertible element $a$ of a Banach algebra $A$, with radius $\frac{1}{\|a^{-1}\|}$, is contained inside the open set of all invertible elements, $G(A)$ in $A$. An invertible element $a$ of a Banach algebra $A$ is said to satisfy BOBP (Biggest Open Ball Property) if the boundary of the ball $B\left( a,\frac{1}{\|a^{-1}\|}\right)$ intersects the set of non invertible elements in $A$. We say a Banach algebra $A$ satisfies BOBP if every $a$ in $G(A)$ satisfies BOBP.\\ The origin of this problem is connected with condition spectra and almost multiplicative functionals. We see that, in general, uniform algebras and $C$*-algebras satisfy BOBP but group algebras need not.

On the open ball centered at an invertible element of a Banach algebra.

Cupples I Room 218

The open ball centered at an invertible element $a$ of a Banach algebra $A$, with radius $\frac{1}{\|a^{-1}\|}$, is contained inside the open set of all invertible elements, $G(A)$ in $A$. An invertible element $a$ of a Banach algebra $A$ is said to satisfy BOBP (Biggest Open Ball Property) if the boundary of the ball $B\left( a,\frac{1}{\|a^{-1}\|}\right)$ intersects the set of non invertible elements in $A$. We say a Banach algebra $A$ satisfies BOBP if every $a$ in $G(A)$ satisfies BOBP.\\ The origin of this problem is connected with condition spectra and almost multiplicative functionals. We see that, in general, uniform algebras and $C$*-algebras satisfy BOBP but group algebras need not.