Publicado

1968-10-01

Algebraic theory of atkinson operators

Palabras clave:

Linear space, endomorphisms, operator, numbers, hypothesis (es)

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Autores/as

  • Harro Heuser

Notations: In this paper E denotes a linear space, δ(E) the set of all endomorphisms  of E , L(E) the set of all continuous endomorphisms of E if E is equipped with a vector  space topology.  If  T ∈δ (E),  then                        

N(T) ={x:    Tx= 0}

B(T) = {Tx:  x   ∈ E }

∝ (T) =  dim N (T)

β (T) = codim B(T)

Based on the wo rk of Fredholm,  F. Riesz and Noether, Atkinson defined the abstract  concept of a Fredholm operador on a Banach space E : T ∈ 𝓁( E) is called a Fredholm  operator if ∝ (T) and β(T)are both finite and B(T) is closed. As was shown later by Kato, β (T)  <∞ already implies that B(T) is close. When considering continuous operators T on a Banach space E for wich only one of the numbers  ∝ (T) β (T) was supposed to be finite, Atkinson remarked that the hypothesis B(T) is closedil was not sufficient to establish a satisfying theory. He therefore introduced the stronger hypothesis of relative regularity: T ∈ 𝓁( E)  is calles relatively regular if there exists a S ∈ 𝓁( E)  such that

T S T = T

Cómo citar

APA

Heuser, H. (1968). Algebraic theory of atkinson operators. Revista Colombiana de Matemáticas, 2(4), 137–143. https://revistas.unal.edu.co/index.php/recolma/article/view/31541

ACM

[1]
Heuser, H. 1968. Algebraic theory of atkinson operators. Revista Colombiana de Matemáticas. 2, 4 (oct. 1968), 137–143.

ACS

(1)
Heuser, H. Algebraic theory of atkinson operators. rev.colomb.mat 1968, 2, 137-143.

ABNT

HEUSER, H. Algebraic theory of atkinson operators. Revista Colombiana de Matemáticas, [S. l.], v. 2, n. 4, p. 137–143, 1968. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/31541. Acesso em: 29 mar. 2024.

Chicago

Heuser, Harro. 1968. «Algebraic theory of atkinson operators». Revista Colombiana De Matemáticas 2 (4):137-43. https://revistas.unal.edu.co/index.php/recolma/article/view/31541.

Harvard

Heuser, H. (1968) «Algebraic theory of atkinson operators», Revista Colombiana de Matemáticas, 2(4), pp. 137–143. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/31541 (Accedido: 29 marzo 2024).

IEEE

[1]
H. Heuser, «Algebraic theory of atkinson operators», rev.colomb.mat, vol. 2, n.º 4, pp. 137–143, oct. 1968.

MLA

Heuser, H. «Algebraic theory of atkinson operators». Revista Colombiana de Matemáticas, vol. 2, n.º 4, octubre de 1968, pp. 137-43, https://revistas.unal.edu.co/index.php/recolma/article/view/31541.

Turabian

Heuser, Harro. «Algebraic theory of atkinson operators». Revista Colombiana de Matemáticas 2, no. 4 (octubre 1, 1968): 137–143. Accedido marzo 29, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/31541.

Vancouver

1.
Heuser H. Algebraic theory of atkinson operators. rev.colomb.mat [Internet]. 1 de octubre de 1968 [citado 29 de marzo de 2024];2(4):137-43. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/31541

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