The paper is organized as follows: Sections 2, 3, and 4 contain facts from the theories of, respectively, unitarily
invariant random matrices, free probability, and entanglement, which are used later in the paper.
(2) If b [not member of] ran(I - A), then for any 1 [member of] R, [C.sub.[psi],[phi]] is unitarily
equivalent to [e.sup.it][C.sub.[psi],[phi]].
Let M be an internal [C.sup.*]-algebra and let [??], [??] be unitarily
equivalent projections in [??].
Concerning Induction Problem (I), a special case is the unitary induction [Ind.sup.G.sub.H]([tau]) from the trivial one-dimensional representation [tau] = 1 of H, which is unitarily
equivalent to the regular representation of G on [L.sup.2](G/H) if G/H admits a G-invariant Radon measure.
It is worth mentioning that if [kappa] = [infinity], then any weighted shift [S.sub.[lambda]] on [T.sub.[infinity],[infinity]] with nonzero weights is unitarily
equivalent to an injective composition operator in an [L.sup.2]-space over a [sigma]-finite measure space (cf.
Practical interest in the polar decomposition stems mainly from the fact that the unitary polar factor of A is the nearest unitary matrix to A in any unitarily
invariant norm .
For one, Congress is a "they," not an "it" that can unitarily
In LTT the classification is unitarily
made by resort to the noun "unit" ("unitate") accompanied by the specific determinant of each unit in order to mark the distinctive classification elements: ("accommodation", "hotelier", "with hotelier activity", "touristic").
Although the term "crusade" did not exist in the eleventh century, and was not, until the modern era, the unitarily
accepted term for an enterprise arising from the reconquest of Mediterranean Christian lands from the Muslims, it can safely be assumed that crusading had a fundamentum in re, a foundation in reality, prior to the activity of men's minds to name it, conceptualize it, and give it an intellectual content.
In turn, the revenue from this increased activity has almost unitarily
been pumped back into national infrastructure development creating a multibillion dollar market for companies ranging from contractors to consultants.
As regards the indicator net tons kilometer, we consider that t does not reflect unitarily
and consequently the real volume of activity and, subsequently we did not use it in our calculations.