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dc.contributor.advisorDoran, Robert S.
dc.contributor.authorTiller, Albert Wayneen_US
dc.date.accessioned2019-10-11T15:11:02Z
dc.date.available2019-10-11T15:11:02Z
dc.date.created1972en_US
dc.date.issued1972en_US
dc.identifieraleph-255161en_US
dc.identifier.urihttps://repository.tcu.edu/handle/116099117/33821
dc.description.abstractIn 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.extentv, 39 leaves, bounden_US
dc.format.mediumFormat: Printen_US
dc.language.isoengen_US
dc.relation.ispartofTexas Christian University dissertationen_US
dc.relation.ispartofAS38.T53en_US
dc.subject.lcshBanach algebrasen_US
dc.titleP-commutative Banach *-algebras, involutions, and extensions of pure positive functionalsen_US
dc.typeTexten_US
etd.degree.departmentDepartment of Mathematics
etd.degree.levelDoctoral
local.collegeCollege of Science and Engineering
local.departmentMathematics
local.academicunitDepartment of Mathematics
dc.type.genreDissertation
local.subjectareaMathematics
dc.identifier.callnumberMain Stacks: AS38 .T53 (Regular Loan)
dc.identifier.callnumberSpecial Collections: AS38 .T53 (Non-Circulating)
etd.degree.nameDoctor of Philosophy
etd.degree.grantorTexas Christian University


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