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**Toeplitz** or **Töplitz** may refer to:

- Töplitz, the German name of Toplița, a city in Romania
- Toplița, Hunedoara, a commune in Romania
- Teplice (archaic German:
*Töplitz*), Czech Republic

**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 (1909–1995), co-founder of the Polish Film School
- Kasper T. Toeplitz (born 1960), Polish-French composer
- Otto Toeplitz (1881–1940), German Jewish mathematician

**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, a settlement in southeastern Slovenia
- Toeplitz matrix, a structured matrix with equal values along diagonals
- Toeplitz operator, the compression of a multiplication operator on the circle to the Hardy space
- Toeplitz algebra, the C*-algebra generated by the unilateral shift on the Hilbert space
- Toeplitz Hash Algorithm, used in many network interface controllers
- Hellinger–Toeplitz theorem, an everywhere defined symmetric operator on a Hilbert space is bounded
- Silverman–Toeplitz theorem, characterizing matrix summability methods which are regular
- Toplița (disambiguation)
- Teplice (disambiguation)

**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.

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**C ^{∗}-algebras** are subjects of research in functional analysis, a branch of mathematics. A C*-algebra is a complex algebra

**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:

- A *-representation of
*A*on some auxiliary Hilbert space*K*followed by - An operator map of the form
*T*→*VTV**.

**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 *l*^{2}(**N**). Taking *l*^{2}(**N**) to be the Hardy space *H*^{2}, the Toeplitz algebra consists of elements of the form

**Toplița** is a city in Harghita County.