Nuclear maps and modular structures. 1. General properties

Buchholz, Detlev; D'Antoni, Claudio; Longo, Roberto

doi:10.1016/0022-1236(90)90104-S

Nuclear maps and modular structures. 1. General properties

1989

27 pages

Published in:

J.Funct.Anal. 88 (1990) 233-250

DOI:

10.1016/0022-1236(90)90104-S

View in:

AMS MathSciNet

reference search43 citations

Citations per year

Abstract: (Elsevier)

We establish a correspondence between the split property of inclusions A ⊂ B of von Neumann algebras and nuclearity properties of the natural embeddings φ p : L ∞ ( A ) → L p ( B ), p = 1, 2, given by the modular theory.

References(23)

Figures(0)

[1]

Positive cones and L p spaces for von Neumann algebras

H. Araki
,
T. Masuda

- Publ.Res.Inst.Math.Sci.Kyoto 18 (1982) 330

[2]

Eléments de Mathématique

N. Bourbaki

[3]

The Universal Structure of Local Algebras

D. Buchholz
(
- Hamburg U.
)
,
K. Fredenhagen
(
- Hamburg U.
)
,
C. D'Antoni
(
- Rome U., La Sapienza, Dip. di Matematica
)

- Commun.Math.Phys. 111 (1987) 123
•
DOI:
- 10.1007/BF01239019

[4]

Nuclear maps and modular structures. II. Applications to Quantum Field Theory, Comm. Math. Phys. (to appear)

D. Buchholz
,
C. D'Antoni
,
R. Longo

[5]

On Noether's Theorem in Quantum Field Theory

- Annals Phys. 170 (1986) 1
•
DOI:
- 10.1016/0003-4916(86)90086-2

[6]

Causal Independence and the Energy Level Density of States in Local Quantum Field Theory

Detlev Buchholz
(
- Hamburg U.
)
,
Eyvind H. Wichmann
(
- UC, Berkeley
)

- Commun.Math.Phys. 106 (1986) 321
•
DOI:
- 10.1007/BF01454978

[7]

On the spatial theory of von Neumann algebras

A. Connes

- J.Funct.Anal. 35 (1980) 153

[8]

Caractérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann

A. Connes

- Annales Inst.Fourier 24 (1974) 4

[9]

Classification des facteurs

A. Connes

- Proc.Symp.Pure Math. 38 (1982) 43

[10]

Property T for von Neumann algebras

A. Connes
,
V. Jones

- Bull.London Math.Soc. 17 (1985) 57

[11]

Homogeneity of the state space of factors of type III 1

A. Connes
,
E. Stormer

- J.Funct.Anal. 28 (1978) 187

[12]

Interpolation by type I factors and the flip automorphism

- J.Funct.Anal. 51 (1983) 361-371
•
DOI:
- 10.1016/0022-1236(83)90018-6

[13]

Standard and split inclusions of von Neumann algebras

- Invent.Math. 75 (1984) 493-536
•
DOI:
- 10.1007/BF01388641

[14]

A positive compact operator

D.H Fremlin

- Manuscr.Math. 15 (1975) 323

[15]

Produits tensoriels topologiques et espaces nucléaires

A. Grothendieck

- Mem.Am.Math.Soc. 16 (1955) 1

[16]

Characterization of particles by Mmeans of local observables in the relativistic quantum theory

Volker Enss
(
- Hamburg U.
)

- Commun.Math.Phys. 45 (1975) 35-52
•
DOI:
- 10.1007/BF01609864

[17]

L p spaces associated with arbitrary von Neumann algebra

U. Haagerup

- Colloq.Internat.CNRS 274 (1979) 175

[18]

Les espaces L p d'une algèbre de von Neumann

M. Hilsum

- J.Funct.Anal. 40 (1981) 151

[19]

Locally Convex Spaces

H. Jarchow

[20]

Remarks on the type of von Neumann algebras of local observables in quantum field theory

R.V Kadison

- J.Math.Phys. 4 (1963) 1511

[21]

Applications of uniform convexity of non commutative L p spaces

H. Kosaki

- Trans.Am.Math.Soc. 283 (1984) 265

[22]

Correspondences

S. Popa

[23]

Theory of Operator Algebras I

M. Takesaki