Abstract Complete unitarity is a natural condition on CFT-type regular vertex operator algebra (VOA), which ensures that its modular tensor category (MTC) unitary. In this paper we show any unitary (conformal) extension $U$ of completely VOA $V$ Our method to relate with Q-system $A_U$ in the $C^*$-tensor $\textrm{Rep}^{\textrm{u}}(V)$ $V$-modules. We also update main result [ 30] cases by show...

In what follows, the symbol X stands for a real Banach space with norm ‖ · ‖ and (normalized) duality mapping J. Moreover, “continuous” means “strongly continuous” and the symbol “→” (“⇀”) means strong (weak) convergence. The symbol R (R+) stands for the set (−∞,∞) ([0,∞)) and the symbols ∂D, intD, D denote the strong boundary, interior and closure of the set D, respectively. An operator T : X ...

in this paper we develop a natural generalization of schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. we prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. we prove that the operators of a dual ov-basis are continuous. we also dene the concepts of bessel, hilbert ov-basis and obt...

In this paper we study the operator inequality φ(X) ≤ X and the operator equation φ(X) = X, where φ is a w∗-continuous positive (resp. completely positive) linear map on B(H). We show that their solutions are in one-to-one correspondence with a class of Poisson transforms on Cuntz-Toeplitz C∗-algebras, if φ is completely positive. Canonical decompositions, ergodic type theorems, and lifting the...