The corona theorem as an operator theorem

Author:
C. F. Schubert

Journal:
Proc. Amer. Math. Soc. **69** (1978), 73-76

MSC:
Primary 47B37; Secondary 46J15

DOI:
https://doi.org/10.1090/S0002-9939-1978-0482355-3

MathSciNet review:
0482355

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Abstract: We provide a short proof of a theorem of W. B. Arveson in operator theory. The conclusion of this theorem is the same as that of the Corona Theorem but the hypotheses are operator theoretic. Our proof yields an exact value for the constant involved. We also comment on this theorem as a new approximation problem.

**[1]**W. B. Arveson,*Interpolation problems in nest algebras*, J. Functional Analysis**20**(1975), 208-233. MR**0383098 (52:3979)****[2]**L. Carleson,*Interpolation by bounded analytic functions and the corona problem*, Ann. of Math. (2)**76**(1962), 547-559. MR**0141789 (25:5186)****[3]**R. G. Douglas,*Banach algebra techniques in operator theory*, Academic Press, New York, 1972. MR**0361893 (50:14335)****[4]**R. G. Douglas, P. S. Muhly and Carl Pearcy,*Lifting commuting operators*, Michigan Math. J.**15**(1968), 385-395. MR**0236752 (38:5046)****[5]**B. Sz.-Nagy and C. Foias,*Dilations des commutants d'operateurs*, C. R. Acad. Sci. Paris Sér. A-B**266**(1968), 493-495. MR**0236755 (38:5049)**

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DOI:
https://doi.org/10.1090/S0002-9939-1978-0482355-3

Article copyright:
© Copyright 1978
American Mathematical Society