In mathematics, the structure space of a commutative Banach algebra is an analog of the spectrum of a C*-algebra. It consists of all multiplicative linear functionals on the algebra. The Gelfand representation of the Banach algebra is a map taking the Banach algebra elements to continuous functions on the structure space.
Famous quotes containing the words space and/or structure:
“To play is nothing but the imitative substitution of a pleasurable, superfluous and voluntary action for a serious, necessary, imperative and difficult one. At the cradle of play as well as of artistic activity there stood leisure, tedium entailed by increased spiritual mobility, a horror vacui, the need of letting forms no longer imprisoned move freely, of filling empty time with sequences of notes, empty space with sequences of form.”
—Max J. Friedländer (18671958)
“One theme links together these new proposals for family policythe idea that the family is exceedingly durable. Changes in structure and function and individual roles are not to be confused with the collapse of the family. Families remain more important in the lives of children than other institutions. Family ties are stronger and more vital than many of us imagine in the perennial atmosphere of crisis surrounding the subject.”
—Joseph Featherstone (20th century)