For $V$, $W$ Banach spaces, is the canonical morphism $B(V) \times_\pi B(W) \to B(V \hat{\otimes}_\pi W)$ continuous, where $B(V):=B(V,V)$ are linear bounded endomorphisms with operator norm? If so, is it also smooth (wrt Michal/Bastiani-differentiability in locally convex spaces)? Does it induce a continuous (smooth) map $GL(V)\times_\pi GL(W) \to GL(V \hat{\otimes}_\pi W)$, where $GL(V)=B(V)^{\times}$.

Edit: The answer to the very first question is yes


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.