All Questions

Consider the following fragment from Takesaki's book "Theory of operator algebra I" (Section III.3 ,p133-134). Why is the boxed line true? I can see that $\epsilon: \widetilde{A}\to A$ is ...

Consider the following fragments in Takesaki's "Theory of operator algebras" (volume I): Question: So, we have an abstract Banach space $F$ with $A \cong F^*$. In Lemma 3.6, one considers ...

I'm reading the book "Theory of operator algebras" by Takesaki. In this book, the $\sigma$-strong$^*$ topology on the space $B(H)$ (bounded operators on the Hilbert space $H$) is defined (...

Let $T\in B(\mathcal{H} \otimes \mathcal{H})$ where $\mathcal{H}$ is a Hilbert space. We can define operators $$T_{[12]}= T \otimes 1;\quad T_{[23]}= 1 \otimes T$$ and if $\Sigma: \mathcal{H} \otimes \...

Consider (abstract) von Neumann algebras topologised by their weak*-topology arising from the unique predual. In the theory of topological vector spaces, there is a natural notion of an inductive ...