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In this paper, we investigate derivations on the noncommutative Banach algebra L∞ 0 (ω)∗ equipped with an Arens product. As a main result, we prove the Singer-Wermer conjecture for the noncommutative Banach algebra L∞ 0 (ω)∗. We then show that a derivation on L∞ 0 (ω)∗ is continuous if and only if its restriction to rad(L∞ 0 (ω)∗) is continuous. We also prove that there is no nonzero centralizing derivation on L∞ 0 (ω)∗.
Finally, we prove that the space of all inner derivations of L∞ 0 (ω)∗ is continuously homomorphic to the space L∞ 0 (ω)∗/L1(ω).
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참고문헌 (20)
참고문헌 신청
A. I. Singh / 1999 / L∞0 (G)? as the second dual of the group algebra L1(G) with a locally convex toplogy / Michigan Math. J 46 (1) : 143 ~ 150
A. M. Sinclair / 1969 / Continuous derivations on Banach algebras / Proc. Amer. Math. Soc 20 (1) : 166 ~ 170
A. R. Medghalchi / 1992 / The second dual algebra of a hypergroup / Math. Z 210 (4) : 615 ~ 624
A. T. Lau / 1990 / Concerning the second dual of the group algebra of a locally compact group / J. London Math. Soc 41 (3) : 445 ~ 460
B. E. Johnson / 1969 / Continuity of derivations on commutative algebras / Amer. J. Math 91 : 1 ~ 10
A. M. Sinclair / 1969 / Continuous derivations on Banach algebras / Proc. Amer. Math. Soc 20 (1) : 166 ~ 170
A. R. Medghalchi / 1992 / The second dual algebra of a hypergroup / Math. Z 210 (4) : 615 ~ 624
A. T. Lau / 1990 / Concerning the second dual of the group algebra of a locally compact group / J. London Math. Soc 41 (3) : 445 ~ 460
B. E. Johnson / 1969 / Continuity of derivations on commutative algebras / Amer. J. Math 91 : 1 ~ 10
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