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3 votes
1 answer
145 views

positive functional on Banach *-algebra (with appro. identity) is continuous?

Theorem (N. Th.Varopoulos): Let $\mathcal{B}$ be a Banach *-algebra with a bounded approximate identity. Then every positive functional $T$ on $\mathcal{B}$ is continuous. I think this theorem is prov …
1 vote
0 answers
79 views

In which Sobolev spaces nonlinear wave equation is locally well-posed?

We consider nonlinear wave equation as follows: $$\partial_t^2 \psi - \Delta \psi = \pm |\psi|^{2\sigma} \psi, \quad ( \psi(0, \cdot),\psi_t(0,\cdot))=(\psi_0,\psi_1)$$ where $\sigma \in \mathbb N, …