Geodesic
Functions from the Schoenberg class $\mathscr T$ act in the cone of dissipative elements of a Banach algebra.~II
Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 423-430

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The functional calculus of several commuting dissipative elements of a complex Banach algebra with identity, first introduced in the preceding work by the author, is developed. Uniqueness, continuity, and stability theorems, composite function theorems, and a formula for the resolvent are established. Applications to the theory of sectorial operators in Hilbert space are given. 
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     author = {A. R. Mirotin},
     title = {Functions from the {Schoenberg} class $\mathscr T$ act in the cone of dissipative elements of a {Banach} {algebra.~II}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {423--430},
     publisher = {mathdoc},
     volume = {64},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a10/}
}
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A. R. Mirotin. Functions from the Schoenberg class $\mathscr T$ act in the cone of dissipative elements of a Banach algebra.~II. Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 423-430. http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a10/