General Theory of Banach Algebra. By C.E. Rickart. Pp. 394. 79s. 1960. (Van Nostrand, London)

Determine the value of the variable in each equation.

Basic Algebra = 代数学入門

The Jacobi inversion theorem leads to functions of several variables with many periods. So, we are led to the problem of developing a theory of them which is analogous to the theory of elliptic functions. First of all, we need to give an introduction to the theory of functions of several complex variables. In this chapter, we give an elementary introduction which essentially follows Weierstrass. One of the main topics will be the proof of the theorem that any meromorphic function on ℂn can be written as a quotient of two entire functions. Weierstrass called this a very difficult problem. The first proof was given by Poincare. In the case n = 1, it is not difficult to show this by means of the theory of Weierstrass products, even for arbitrary domains D ⊂ ℂ instead of ℂ. The case n > 1 is more involved, since the zero sets and pole sets of analytic functions of several complex variables are not discrete.

Analytic Functions of Several Complex Variables

https://www.ams.org/proc/1997-125-09/S0002-9939-97-04073-2/S0002-9939-97-04073-2.pdf

Local automorphisms and derivations on $\mathcal{B}(H)$

Spectrum-preserving linear maps

/pdf/a-characterization-of-maximal-ideals-in-commutative-banach-32z63tyi81.pdf

A characterization of maximal ideals in commutative Banach algebras

/pdf/a-characterization-of-multiplicative-linear-functionals-in-4ddtshr2p6.pdf

A characterization of multiplicative linear functionals in complex Banach algebras

/pdf/on-joint-spectra-of-commuting-families-of-operators-4nhvyjpxre.pdf

Wiesław Żelazko

Papers

A characterization of maximal ideals in commutative Banach algebras

A characterization of multiplicative linear functionals in complex Banach algebras

On joint spectra of commuting families of operators

Metric generalizations of Banach algebras

On the locally bounded and m-convex topological algebras