 | Look up Toeplitz matrix in Wiktionary, the free dictionary. |
Toeplitz or Töplitz may refer to:
| Look up Toeplitz matrix in Wiktionary, the free dictionary. |
Toeplitz or Töplitz may refer to:
Toplița is a commune in Hunedoara County, Romania. It is composed of eight villages: Curpenii Silvașului, Dăbâca (Doboka), Dealu Mic (Párosza), Goleș (Golles), Hășdău (Hosdó), Mosoru (Moszor), Toplița and Vălari (Valár).
Teplice ; Teplice-Šanov until 1948 is a statutory city in the Ústí nad Labem Region of the Czech Republic, the capital of Teplice District. It is the state's second largest spa town, after Karlovy Vary.
Jerzy Toeplitz AO was born in 1909 in Kharkiv. He was educated in Warsaw. After World War II he was the co-founder of the Polish Film School, and later took up an appointment in Australia for the Film and TV School.
Kasper T. Toeplitz is a French composer and musician of Polish origin, born in 1960. He lives in Paris.
Otto Toeplitz was a German mathematician working in functional analysis.
Dolenjske Toplice is a settlement near Novo Mesto in southeastern Slovenia and is the seat of the Municipality of Dolenjske Toplice. The area is part of the traditional region of Lower Carniola. The municipality is now included in the Southeast Slovenia Statistical Region. The town lies on the Sušica River, which joins the Krka 2 km north of town. It is a spa town known for its thermal baths established in 1658 by the Counts of Auersperg.
In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant. For instance, the following matrix is a Toeplitz matrix:
In operator theory, a Toeplitz operator is the compression of a multiplication operator on the circle to the Hardy space.
 | This disambiguation page lists articles associated with the title Toeplitz. If an internal link led you here, you may wish to change the link to point directly to the intended article. |
C∗-algebras are subjects of research in functional analysis, a branch of mathematics. A C*-algebra is a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties:
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations.
In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized. This is extremely useful because computations involving a diagonalizable matrix can often be reduced to much simpler computations involving the corresponding diagonal matrix. The concept of diagonalization is relatively straightforward for operators on finite-dimensional vector spaces but requires some modification for operators on infinite-dimensional spaces. In general, the spectral theorem identifies a class of linear operators that can be modeled by multiplication operators, which are as simple as one can hope to find. In more abstract language, the spectral theorem is a statement about commutative C*-algebras. See also spectral theory for a historical perspective.
In functional analysis, a branch of mathematics, a unitary operator is a surjective bounded operator on a Hilbert space preserving the inner product. Unitary operators are usually taken as operating on a Hilbert space, but the same notion serves to define the concept of isomorphism between Hilbert spaces.
In functional analysis, a discipline within mathematics, given a C*-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic *-representations of A and certain linear functionals on A. The correspondence is shown by an explicit construction of the *-representation from the state. It is named for Israel Gelfand, Mark Naimark, and Irving Segal.
In mathematics, especially functional analysis, a self-adjoint element of a C*-algebra is called positive if its spectrum consists of non-negative real numbers. Moreover, an element of a C*-algebra is positive if and only if there is some in such that . A positive element is self-adjoint and thus normal.
In functional analysis, a branch of mathematics, the Hellinger–Toeplitz theorem states that an everywhere-defined symmetric operator on a Hilbert space with inner product is bounded. By definition, an operator A is symmetric if
In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators, and consideration may be given to nonlinear operators. The study, which depends heavily on the topology of function spaces, is a branch of functional analysis.
In mathematics and functional analysis a direct integral is a generalization of the concept of direct sum. The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras. The concept was introduced in 1949 by John von Neumann in one of the papers in the series On Rings of Operators. One of von Neumann's goals in this paper was to reduce the classification of von Neumann algebras on separable Hilbert spaces to the classification of so-called factors. Factors are analogous to full matrix algebras over a field, and von Neumann wanted to prove a continuous analogue of the Artin–Wedderburn theorem classifying semi-simple rings.
In mathematics, particularly in operator theory, Wold decomposition or Wold–von Neumann decomposition, named after Herman Wold and John von Neumann, is a classification theorem for isometric linear operators on a given Hilbert space. It states that every isometry is a direct sum of copies of the unilateral shift and a unitary operator.
In mathematics, Stinespring's dilation theorem, also called Stinespring's factorization theorem, named after W. Forrest Stinespring, is a result from operator theory that represents any completely positive map on a C*-algebra as a composition of two completely positive maps each of which has a special form:
Teplice is a city in the Ústí nad Labem Region and capital of the Teplice District, Czech Republic.
In the theory of von Neumann algebras, the Kaplansky density theorem, due to Irving Kaplansky, is a fundamental approximation theorem. The importance and ubiquity of this technical tool led Gert Pedersen to comment in one of his books that,
In mathematics, and specifically in operator theory, a positive-definite function on a group relates the notions of positivity, in the context of Hilbert spaces, and algebraic groups. It can be viewed as a particular type of positive-definite kernel where the underlying set has the additional group structure.
In operator algebras, the Toeplitz algebra is the C*-algebra generated by the unilateral shift on the Hilbert space l2(N). Taking l2(N) to be the Hardy space H2, the Toeplitz algebra consists of elements of the form
Toplița is a city in Harghita County.