On the Taylor spectrum of left-right multipliers

Harte, Robin; Hernández, Carlos

doi:10.1090/S0002-9939-98-04116-1

On the Taylor spectrum of left-right multipliers
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by Robin Harte and Carlos Hernández PDF

Proc. Amer. Math. Soc. 126 (1998), 397-404 Request permission

Abstract:

The Taylor spectrum of a mixed pair of multiplication operators is determined on an ultraprime Banach algebra.

References

Raúl E. Curto, Applications of several complex variables to multiparameter spectral theory, Surveys of some recent results in operator theory, Vol. II, Pitman Res. Notes Math. Ser., vol. 192, Longman Sci. Tech., Harlow, 1988, pp. 25–90. MR 976843
Raúl E. Curto and Lawrence A. Fialkow, The spectral picture of $(L_A,R_B)$, J. Funct. Anal. 71 (1987), no. 2, 371–392. MR 880986, DOI 10.1016/0022-1236(87)90010-3
R.E. Curto and C. Hernández G., A joint spectral characterization of primeness for $C^{*}$ algebras, Proc. Amer. Math. Soc. (to appear).
R. E. Harte, Spectral mapping theorems, Proc. Roy. Irish Acad. Sect. A 72 (1972), 89–107. MR 326394
R. E. Harte, Tensor products, multiplication operators and the spectral mapping theorem, Proc. Roy. Irish Acad. Sect. A 73 (1973), 285–302. MR 328642
R. E. Harte, Invertibility, singularity and Joseph L. Taylor, Proc. Roy. Irish Acad. Sect. A 81 (1981), no. 1, 71–79. MR 635581
Robin Harte, Almost exactness in normed spaces, Proc. Amer. Math. Soc. 100 (1987), no. 2, 257–265. MR 884463, DOI 10.1090/S0002-9939-1987-0884463-7
R.E. Harte, Invertibility and singularity (Dekker New York 1988).
Robin Harte, Taylor exactness and Kato’s jump, Proc. Amer. Math. Soc. 119 (1993), no. 3, 793–801. MR 1152982, DOI 10.1090/S0002-9939-1993-1152982-7
Martin Mathieu, Elementary operators on prime $C^*$-algebras. I, Math. Ann. 284 (1989), no. 2, 223–244. MR 1000108, DOI 10.1007/BF01442873
Joseph L. Taylor, A joint spectrum for several commuting operators, J. Functional Analysis 6 (1970), 172–191. MR 0268706, DOI 10.1016/0022-1236(70)90055-8