Dixmier's representation theorem of central double centralizers on Banach algebras

Author:
Sin-ei Takahasi

Journal:
Trans. Amer. Math. Soc. **253** (1979), 229-236

MSC:
Primary 46H15

DOI:
https://doi.org/10.1090/S0002-9947-1979-0536944-3

MathSciNet review:
536944

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The present paper is devoted to a representation theorem of central double centralizers on a complex Banach algebra with a bounded approximate identity. In particular, our result implies the representation theorem of the ideal center of an arbitrary -algebra established by J. Dixmier.

**[1]**R. J. Archbold,*Density theorems for the centre of a 𝐶*-algebra*, J. London Math. Soc. (2)**10**(1975), 189–197. MR**0380431**, https://doi.org/10.1112/jlms/s2-10.2.189**[2]**Robert C. Busby,*On structure spaces and extensions of 𝐶*-algebras*, J. Functional Analysis**1**(1967), 370–377. MR**0225176****[3]**Philip C. Curtis Jr. and Alessandro Figà-Talamanca,*Factorization theorems for Banach algebras*, Function Algebras (Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965) Scott-Foresman, Chicago, Ill., 1966, pp. 169–185. MR**0203500****[4]**John Dauns and Karl Heinrich Hofmann,*Representation of rings by sections*, Memoirs of the American Mathematical Society, No. 83, American Mathematical Society, Providence, R.I., 1968. MR**0247487****[5]**John W. Davenport,*Multipliers on a Banach algebra with a bounded approximate identity*, Pacific J. Math.**63**(1976), no. 1, 131–135. MR**0412810****[6]**J. Dixmier,*Ideal center of a 𝐶*-algebra*, Duke Math. J.**35**(1968), 375–382. MR**0230138****[7]**Kichi-suke Saito,*A characterization of double centralizer algebras of Banach algebras*, Sci. Rep. Niigata Univ. Ser. A**11**(1974), 5–11. MR**0341094****[8]**Charles E. Rickart,*General theory of Banach algebras*, The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR**0115101**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
46H15

Retrieve articles in all journals with MSC: 46H15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0536944-3

Article copyright:
© Copyright 1979
American Mathematical Society