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Suppose that X is a vector space over the field of complex or real numbers. Then the set of all linear functionals on X forms a vector space called the algebraic conjugate ...

The region 0<sigma<1, where sigma is defined as the real part of a complex number s=sigma+it. All nontrivial zeros (i.e., those not at negative even integers) of the Riemann ...

Functional analysis is a branch of mathematics concerned with infinite-dimensional vector spaces (mainly function spaces) and mappings between them. The spaces may be of ...

A finitely generated discontinuous group of linear fractional transformations z->(az+b)/(cz+d) acting on a domain in the complex plane. The Apollonian gasket corresponds to a ...

Let A be a commutative complex Banach algebra. The space of all characters on A is called the maximal ideal space (or character space) of A. This space equipped with the ...

A Banach space X is called minimal if every infinite-dimensional subspace Y of X contains a subspace Z isomorphic to X. An example of a minimal Banach space is the Banach ...

Let A be a C^*-algebra. An element a in A is called positive if a=a* and sp(a) subset= R^+, or equivalently if there exists an element b in A such that a=bb^*. For example, ...

Let A be a C^*-algebra. An element a in A is called self-adjoint if a^*=a. For example, the real functions of the C^*-algebra of C([a,b]) of continuous complex-valued ...

If M^n is a finite simplicial complex of dimension n>=5 that has the homotopy type of the sphere S^n and is locally piecewise linearly homeomorphic to the Euclidean space ...

Let A be a commutative ring, let C_r be an R-module for r=0, 1, 2, ..., and define a chain complex C__ of the form C__:...|->C_n|->C_(n-1)|->C_(n-2)|->...|->C_2|->C_1|->C_0. ...