相关论文: Kadison-Singer from mathematical physics: An intro…
We analyse possibility to extend a quantum operation (sub-unital normal CP linear map on the algebra $B(H)$ of bounded operators on a separable Hilbert space $H$) to the space of all operators on $H$ relatively bounded w.r.t. a given…
Consider $d$ disjoint closed subintervals of the unit interval and consider an orientation preserving expanding map which maps each of these subintervals to the whole unit interval. The set of points where all iterates of this expanding map…
We give embedding theorems for weighted Bergman-Orlicz spaces on the ball and then apply our results to the study of composition operators in this context. As one of the motivations of this work, we show that there exist some weighted…
The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields…
Kadison and Kastler introduced a natural metric on the collection of all C*-subalgebras of the bounded operators on a separable Hilbert space. They conjectured that sufficiently close algebras are unitarily conjugate. We establish this…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
The need for a mathematically rigorous quantization procedure of singular spaces and incomplete motions is pointed out in connection with quantum cosmology. We put our previous suggestion for such a procedure, based on the theory of induced…
In this paper, Hardy's uncertainty principle and unique continuation properties of Schrodinger equations with operator potentials in Hilbert space-valued classes are obtained. Since the Hilbert space H and linear operators are arbitrary, by…
The Hilbert transform is essentially the \textit{only} singular operator in one dimension. This undoubtedly makes it one of the the most important linear operators in harmonic analysis. The Hilbert transform has had a profound bearing on…
Assuming the continuum hypothesis, we prove that B(H) has a pure state whose restriction to any masa is not pure. This resolves negatively an old conjecture of Anderson.
A result of Akemann, Anderson, and Pedersen states that if a sequence of pure states of a C*-algebra A approaches infinity in a certain sense, then there is a MASA B such that each of the states has the unique extension property with…
We derive a description of the family of canonical selfadjoint extensions of the operator of multiplication in a de Branges space in terms of singular rank-one perturbations using distinguished elements from the set of functions associated…
We construct complete sets of (open and closed string) covariant coherent state and mass eigenstate vertex operators in bosonic string theory. By minimally extending the standard definition of coherent states so as to include the string…
We consider an abstract sequence $\{A_n\}_{n=1}^\infty$ of closed symmetric operators on a separable Hilbert space $\mathcal{H}$. It is assumed that all $A_n$'s have equal deficiency indices $(k,k)$ and thus self-adjoint extensions…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
We develop a duality theory for unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency…
We discuss a rigid string model proposed by Casalbuoni and Longhi. Constraints for the massive states are solved to find the physical states and the mass spectrum. We also find its supersymmetric extension with the kappa symmetry. The…
For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension space ${\mathcal D(S)}$ consisting of…
We present a construction of Hermitian operators and quantum states labelled by strings from a finite field. The distance between these operators or states is then simply related (typically, proportional) to the Hamming distance between…
Let $L_0$ be a densely defined minimal linear operator in a Hilbert space $H$. We prove theorem that if there exists at least one correct extension $L_S$ of $L_0$ with the property $D(L_S)=D(L_S^*)$, then we can describe all correct…