Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Given $\cal{A},\cal{B}$ two dense $*$-algebras of two $C^*$-algebras $A$ and $B$ respectively, together with a $*$-mapalgebra homomorphism$f:\cal{A} \to \cal{B}$, is it clear that $f$ extends to a bounded linear operator $f:A \to B$?
Given $\cal{A},\cal{B}$ two dense $*$-algebras of two $C^*$-algebras $A$ and $B$ respectively, together with a $*$-map$f:\cal{A} \to \cal{B}$, is it clear that $f$ extends to a bounded linear operator $f:A \to B$?
Given $\cal{A},\cal{B}$ two dense $*$-algebras of two $C^*$-algebras $A$ and $B$ respectively, together with a $*$-algebra homomorphism$f:\cal{A} \to \cal{B}$, is it clear that $f$ extends to a bounded linear operator $f:A \to B$?
Extending maps from dense $*$-algebras of $C^*$-algebras
Given $\cal{A},\cal{B}$ two dense $*$-algebras of two $C^*$-algebras $A$ and $B$ respectively, together with a $*$-map $f:\cal{A} \to \cal{B}$, is it clear that $f$ extends to a bounded linear operator $f:A \to B$?
