Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. An approximate identity is a right approximate identity which is also a left approximate identity. For C*-algebras, a right approximate identity is the same as an approximate identity. Every C*-algebra has an approximate identity of positive elements of norm <= 1; indeed, the net of all positive elements of norm <= 1; in A with its natural order always suffices. This is called the canonical approximate identity of a C*-algebra. Approximate identities of C*-algebras are not unique. For example, for compact operators acting on a Hilbert space, the net consisting of finite rank projections would be another approximate identity. An approximate identity in a convolution algebra plays the same role as a sequence of function approximations to the Dirac delta function. For example the Fejer kernels of Fourier series theory give rise to an approximate identity.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.