Partial multiplication of operators in rigged hilbert spaces

Integral Equations and Operator Theory

Volumn 51, Issue 4, 2005, Pages 583-600

  Trapani, Camillo ^a   Tschinke, Francesco ^a  

^a UNIVERSITY OF PALERMO   (Italy)

Author keywords

Primary 47L60; Secondary 46C50

Indexed keywords

EID: 18244404808     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00020-002-1263-z     Document Type: Article

References (24)

1. G. Lassner, Topological algebras and their applications in quantum statistics, Wiss. Z. KMU, Leipzig, Math.-Nat. R. 6 (1981), 572-595.
2. G. Lassner, Algebras of Unbounded Operators and Quantum Dynamics, Physica, 124A (1984), 471-480.
3. K. Schmüdgen, Unbounded Operator Algebras and Representations Theory, OT vol. 37, Birkhäuser, Basel, 1990.
4. C. Trapani, Quasi *-algebras of operators and their applications, Reviews Math. Phys. 7 (1995) 1303-1332.
5. G. Epifanio and C. Trapani, Quasi *-Algebras valued Quantized Fields, Ann. Inst. H. Poincaré 46, (1987) 175-185.
6. M. Oberguggenberger, Multiplication of distributions and applications to partial differential equations, Pitman Research Notes in Mathematics Series, n. 259, Longman, Harlow, 1992.
7. A. Russo and C. Trapani, Quasi *-algebras and multiplication of distributions, J. Math. Anal. Appl. 215 (1997), 423-442.
8. K.D. Kürsten, The completion of the maximal Op *-algebra on a Fréchet domain, Publ. RIMS, Kyoto Univ., 22 (1986), 151-175.
9. G. Epifanio and C. Trapani, Partial *-algebras and Volterra convolution of distribution kernels, J. Math. Phys. 32 (1991), 1096-1101.
10. J.-P. Antoine and W. Karwowski, Partial *-Algebras of Closed Linear Operators in Hilbert Space, Publ. RIMS, Kyoto Univ. 21 (1985), 205-236.
11. J.-P. Antoine and W. Karwowski, Interpolation theory and refinement of nested Hilbert spaces, J. Math. Phys. 22 (1981), 2489-2496.
12. J. Bergh and J. Löfström, Interpolation Spaces, Springer, Berlin, 1976.
13. J.-P. Antoine, A. Inoue and C. Trapani, Partial *-algebras of closable operators: A review, Reviews Math. Phys. 8 (1996), 1-42.
14. J.-P. Antoine, A. Inoue, and C. Trapani, Partial *-Algebras and Their Operator Realizations, Kluwer Academic Publ. , MIA Vol. 553, Dordrecht, 2002.
15. K.D. Kürsten, On algebraic properties of partial algebras, Suppl. Rend. Circ. Mat. Palermo 56 (1998), 111-122.
16. J.-P. Antoine and A. Grossmann, Partial inner product spaces. I. General properties, J. Funct. Analysis 23 (1976), 369-378.
17. J.-P. Antoine and A. Grossmann, Partial inner product spaces. II. Operators, J. Funct. Analysis 23 (1976), 379-391.
18. J.-P. Antoine, Partial inner product spaces. III. Compatibility relations revisited, J. Math. Phys. 21 (1980), 268-279.
19. J.-P. Antoine, Portial inner product spaces. IV. Topological considerations, J. Math. Phys. 21 (1980), 2067-2079.
20. M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. I, Academic Press, New York, 1980.
21. R.A. Adams, Sobolev spaces, Academic Press, New York, 1975
22. H. Triebel, Theory of Function Spaces, Birkäueser Verlag, Basel, 1983.
23. H. Brezis, Analisi Funzionale - Teoria e Applicazioni, Liguori, Napoli,1986.
24. G. Lassner, G.A. Lassner and C. Trapani, Canonical commutation relations on the interval, J. Math. Phys, 28 (1987), 174-177.