In the hierarchy of freeness construction, free independence was reduced to tensor independence in the weak sense of convergence of moments. In this paper we show how to reduce free independence to tensor independence in the strong sense. We construct a suitable unital *-algebra of closed operators ‘affiliated’ with a given unital *-algebra and call the associated closure ‘monotone’. Then we pr...

Let Uβ be the special Buekenhout-Metz unital in PG(2, q 2) formed by a union of q conics, where q = pe is an odd prime power. It can be shown that the dimension of the binary code of the corresponding unital design Uβ is less than or equal to q3 + 1− q. Baker and Wantz conjectured that equality holds. We prove that the aforementioned dimension is greater than or equal to q3(1− 1 p ) + q 2 p .

For every integer d ≥ 1, there is a unital closed subalgebra A d ⊂ B(H) with similarity degree equal precisely to d, in the sense of our previous paper. This means that for any unital homomorphism u: A d → B(H) we have u cb ≤ Ku d with K > 0 independent of u, and the exponent d in this estimate cannot be improved. The proof that the degree is larger than d − 1 crucially uses an upper bound for ...

In an attempt to propose more general conditions for decoherence occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital C⁎-algebras, with a particular focus gapped which the transient portion arising dynamical system can be separated from persistent one. After some results, first devote our attention abelian case by investigating ⁎-endomorp...

We give a general construction for unitals of order q admitting an action of SU(2, q). The construction covers the classical hermitian unitals, Grüning’s unitals in Hall planes and at least one unital of order four where the translation centers fill precisely one block. For the latter unital, we determine the full group of automorphisms and show that there are no group-preserving embeddings int...