dc.contributor.advisor | Doran, Robert S. | |
dc.contributor.author | Tiller, Albert Wayne | en_US |
dc.date.accessioned | 2019-10-11T15:11:02Z | |
dc.date.available | 2019-10-11T15:11:02Z | |
dc.date.created | 1972 | en_US |
dc.date.issued | 1972 | en_US |
dc.identifier | aleph-255161 | en_US |
dc.identifier.uri | https://repository.tcu.edu/handle/116099117/33821 | |
dc.description.abstract | In this dissertation a class of *-algebras is defined which generalizes the class of commutative *-algebras. This is accomplished as follows. Let A be a complex *-algebra. If f is a positive functional on A, let I_f= {x in A: f(x*x) = 0} be the corresponding left ideal of A. Set P = intersection I_f, where the intersection is over all positive functionals on A. Then A is called P-commutative if xy - yx is in P for all x, y in A. Examples are given of noncommutative *-algebras which are P-commutative and many results are obtained for P-commutative Banach *-algebras which extend results known for commutative Banach *-algebras. Among them are the following: If A^2 = A, then every positive functional on A is continuous. If A has an approximate identity, then a nonzero positive functional on A is a pure state if and only if it is multiplicative. If A is symmetric, then the spectral radius in A is a continuous algebra semi-norm. Two theorems, not concerned with P-commutative *-algebras, are proven in Chapter III. The first says that, in a Banach *-algebra which is spanned by a finite number of its maximal commutative *-subalgebras, local continuity of the involution implies continuity of the involution. The second theorem is an extension theorem for pure positive functionals. | |
dc.format.extent | v, 39 leaves, bound | en_US |
dc.format.medium | Format: Print | en_US |
dc.language.iso | eng | en_US |
dc.relation.ispartof | Texas Christian University dissertation | en_US |
dc.relation.ispartof | AS38.T53 | en_US |
dc.subject.lcsh | Banach algebras | en_US |
dc.title | P-commutative Banach *-algebras, involutions, and extensions of pure positive functionals | en_US |
dc.type | Text | en_US |
etd.degree.department | Department of Mathematics | |
etd.degree.level | Doctoral | |
local.college | College of Science and Engineering | |
local.department | Mathematics | |
local.academicunit | Department of Mathematics | |
dc.type.genre | Dissertation | |
local.subjectarea | Mathematics | |
dc.identifier.callnumber | Main Stacks: AS38 .T53 (Regular Loan) | |
dc.identifier.callnumber | Special Collections: AS38 .T53 (Non-Circulating) | |
etd.degree.name | Doctor of Philosophy | |
etd.degree.grantor | Texas Christian University | |