A proof is given that an invertible and a unitary operator can be used to reproduce the effect of a q-deformed commutator of annihilation and creation operators. In other words, the original annihilation and creation operators are mapped into new operators, not conjugate to each other, whose standard commutator equals the identity plus a correction proportional to the original number operator. ...

Relativizing an idea from multiplicity theory, we say that an element x of a von Neumann algebra M is n-divisible if W (x) ∩ M unitally contains a factor of type In. We decide the density of the n-divisible operators, for various n, M, and operator topologies. The most sensitive case is σ-strong density in II1 factors, which is closely related to the McDuff property. We make use of Voiculescu’s...

The Heisenberg evolution of a given unitary operator corresponds classically to a fixed canonical transformation that is viewed through a moving coordinate system. The operators that form the bases of the Weyl representation and its Fourier transform, the chord representation, are, respectively, unitary reflection and translation operators. Thus, the general semiclassical study of unitary opera...

|We extend the characteristic function method (CFM) to more general groups, operators, and signal spaces. We show that the extended CFM can be applied to projected unitary operators as well as discrete-time/periodic signals.

We consider unitary analogs of d−dimensional Anderson models on l2(Zd) defined by the product Uω = DωS where S is a deterministic unitary and Dω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman-Molchanov to get exponential estimates o...

Joseph Emerson,1 Robert Alicki,2 and Karol Życzkowski1, 3, 4 Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Wita Stwosza 57, PL 80-952 Gdańsk, Poland Institute of Physics, Jagiellonian University, ul. Reymonta 4, 31-059 Cracow, Poland Center for Thoretical Physics, Polish Academy of Sciences, Al Lot...

De nition. Let (V, 〈 , 〉) be a n-dimensional euclidean vector space and T : V −→ V a linear operator. We will call the adjoint of T , the linear operator S : V −→ V such that: 〈T (u), v〉 = 〈u, S(v)〉 , for all u, v ∈ V . Proposition 1. Let (V, 〈 , 〉) be a n-dimensional euclidean vector space and T : V −→ V a linear operator. The adjoint of T exists and is unique. Moreover, if E denotes an orthon...

When people search for documents, they eventually want content, not words. Hence, search engines should relate documents more by their underlying concepts than by the words they contain. One promising technique to do so is Latent Semantic Indexing (LSI). LSI dramatically reduces the dimension of the document space by mapping it into a space spanned by conceptual indices. Empirically, the number...

The classical second order Lamé equation contains a so-called accessory parameter B. In this paper we study for which values of B the Lamé equation has a monodromy group which is conjugate to a subgroup of SL(2,R) (unitary monodromy with indefinite hermitian form). We refomulate the problem as a spectral problem and give an asymptotic expansion for the spectrum.

Denote by w(A) the numerical radius of a bounded linear operator A acting on Hilbert space. Suppose that A is invertible and that w(A) ≤ 1+ε and w(A−1) ≤ 1+ε for some ε ≥ 0. It is shown that inf{‖A−U‖ : U unitary} ≤ cε for some constant c > 0. This generalizes a result due to J.G. Stampfli, which is obtained for ε = 0. An example is given showing that the exponent 1/4 is optimal. The more gener...