Projective Gravity

Projection Geometry

In [1] and [3] it was pointed out that octonians can replace an infinite dimensional Hilbert space and psi-waves descriptions concerning the states of deuteron which are finite in number. It is then clear that gravity needs projective and projection geometry to be described in a unified way with the three other basic forces of physics.

Direct Model Reference Adaptive Control in Infinite-Dimensional Hilbert Space

Adaptive and Learning Systems ◽

10.1007/978-1-4757-1895-9_22 ◽

1986 ◽

pp. 309-326

Author(s):

John Ting-Yung Wen ◽

Mark J. Balas

Keyword(s):

Hilbert Space ◽

Adaptive Control ◽

Model Reference Adaptive Control ◽

Model Reference ◽

Infinite Dimensional ◽

Direct Model ◽

Model Reference Adaptive

EXTENSION ALGEBRAS OF CUNTZ ALGEBRA, II

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972709000227 ◽

2009 ◽

Vol 80 (1) ◽

pp. 83-90 ◽

Cited By ~ 1

Author(s):

SHUDONG LIU ◽

XIAOCHUN FANG

Keyword(s):

Hilbert Space ◽

Compact Operators ◽

Cuntz Algebra ◽

Infinite Dimensional ◽

Algebra Ii ◽

K Theory ◽

Extension Algebra

AbstractIn this paper, we construct the unique (up to isomorphism) extension algebra, denoted by E∞, of the Cuntz algebra 𝒪∞ by the C*-algebra of compact operators on a separable infinite-dimensional Hilbert space. We prove that two unital monomorphisms from E∞ to a unital purely infinite simple C*-algebra are approximately unitarily equivalent if and only if they induce the same homomorphisms in K-theory.

Partial automorphisms of stable C-algebras and Hilbert C-bimodules

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700010971 ◽

2005 ◽

Vol 79 (3) ◽

pp. 391-398

Author(s):

Kazunori Kodaka

Keyword(s):

Hilbert Space ◽

Compact Operators ◽

Equivalence Classes ◽

Infinite Dimensional ◽

C Algebras ◽

Countably Infinite

AbstractLet A be a C*-algebra and K the C*-algebra of all compact operators on a countably infinite dimensional Hilbert space. In this note, we shall show that there is an isomorphism of a semigroup of equivalence classes of certain partial automorphisms of A ⊗ K onto a semigroup of equivalence classes of certain countably generated A-A-Hilbert bimodules.

The Set of Finite Operators is Nowhere Dense

Canadian Mathematical Bulletin ◽

10.4153/cmb-1989-046-4 ◽

1989 ◽

Vol 32 (3) ◽

pp. 320-326 ◽

Cited By ~ 2

Author(s):

Domingo A. Herrero

Keyword(s):

Hilbert Space ◽

Linear Operator ◽

Bounded Linear Operator ◽

Dense Subset ◽

Bounded Linear ◽

Infinite Dimensional ◽

Dimensional Hilbert Space

AbstractA bounded linear operator A on a complex, separable, infinite dimensional Hilbert space is called finite if for each . It is shown that the class of all finite operators is a closed nowhere dense subset of

The EMM and the Spectral Analysis of a Non Self-adjoint Hamiltonian on an Infinite Dimensional Hilbert Space

Springer Proceedings in Physics - Non-Hermitian Hamiltonians in Quantum Physics ◽

10.1007/978-3-319-31356-6_10 ◽

2016 ◽

pp. 157-166 ◽

Cited By ~ 4

Author(s):

Natalia Bebiano ◽

João da Providência

Keyword(s):

Hilbert Space ◽

Spectral Analysis ◽

Infinite Dimensional ◽

Dimensional Hilbert Space

Canonical commutation relations, the Weierstrass Zeta function, and infinite dimensional Hilbert space representations of the quantum group Uq(sl2)

Journal of Mathematical Physics ◽

10.1063/1.531797 ◽

1996 ◽

Vol 37 (9) ◽

pp. 4203-4218 ◽

Cited By ~ 5

Author(s):

Asao Arai

Keyword(s):

Hilbert Space ◽

Quantum Group ◽

Zeta Function ◽

Canonical Commutation Relations ◽

Infinite Dimensional ◽

Commutation Relations ◽

Dimensional Hilbert Space

A SIMPLE PROOF OF THE FUNDAMENTAL THEOREM ABOUT ARVESON SYSTEMS

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025706002378 ◽

2006 ◽

Vol 09 (02) ◽

pp. 305-314 ◽

Cited By ~ 10

Author(s):

MICHAEL SKEIDE

Keyword(s):

Hilbert Space ◽

Simple Proof ◽

Fundamental Theorem ◽

Hilbert Module ◽

Bounded Operators ◽

Infinite Dimensional ◽

Product Systems ◽

The One

With every E0-semigroup (acting on the algebra of of bounded operators on a separable infinite-dimensional Hilbert space) there is an associated Arveson system. One of the most important results about Arveson systems is that every Arveson system is the one associated with an E0-semigroup. In these notes we give a new proof of this result that is considerably simpler than the existing ones and allows for a generalization to product systems of Hilbert module (to be published elsewhere).

Tomography in Abstract Hilbert Spaces

Open Systems & Information Dynamics ◽

10.1007/s11080-006-9004-4 ◽

2006 ◽

Vol 13 (03) ◽

pp. 239-253 ◽

Cited By ~ 20

Author(s):

V. I. Man'ko ◽

G. Marmo ◽

A. Simoni ◽

F. Ventriglia

Keyword(s):

Hilbert Space ◽

Quantum State ◽

Trace Formula ◽

Hilbert Spaces ◽

Scalar Product ◽

Linear Operators ◽

Infinite Dimensional ◽

Rank One

The tomographic description of a quantum state is formulated in an abstract infinite-dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity, written in terms of over-complete sets of rank-one projectors and of associated Gram-Schmidt operators taking into account their non-orthogonality, are then used to reconstruct a quantum state from its tomograms. Examples of well known tomographic descriptions illustrate the exposed theory.