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## Structure properties of D-R spaces

Autorzy
Seria
Rozprawy Matematyczne tom/nr w serii: 184 wydano: 1981
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Warianty tytułu
Abstrakty
EN

CONTENTS

Introduction................................................................................................................................... 5

Notations.......................................................................................................................... 5

§ 1. Preliminaries........................................................................................................................ 6
1. Right invertible operators.................................................................................................. 6
2. D-R vector spaces.............................................................................................................. 7
3. Basic types of D-R spaces............................................................................................... 7
3.1. Examples............................................................................................................. 7
4. Subspaces.......................................................................................................................... 8
5. Homomorphisms............................................................................................................... 8
5.1 Quotient spaces and homomorphisms......................................................... 10

§2. The general Taylor theorem............................................................................................... 11
1. The elementary Taylor theorem....................................................................................... 11
1.1. Bands of subspaces....................................................................................... 12
2. The general Taylor theorem............................................................................................. 14

§ 3. Structure elements of D-R spaces................................................................................... 17
1. The simple Taylor formula................................................................................................ 17
2. Distinguished subspaces and subspace chains....................................................... 18
2.1. Canonical subspaces of a D-R space........................................................ 18
2.2. The space $D_i$............................................................................................. 19
2.3. The space S...................................................................................................... 19
2.4. The space Q..................................................................................................... 20
3. Extension of the domain of D........................................................................................... 21
4. The structure chain............................................................................................................ 22
5. Components and formal component series................................................................ 23
6. Examples............................................................................................................................. 25

§ 4. The D-R homomorphism theorem.................................................................................. 27
1. The D-R reference space $X_0$..................................................................................... 27
1.1. X(Z) as a $D_0-R_0$ space with $D_D_0$ = X(Z)................................... 28
1.2. The $d_0$-convergence................................................................................ 28
1.3. The Volterra property of $X_0$ and eigenspaces of $D_0$...................... 31
2. $D_D_0$ $\varsubsetneqq$ $X_0(Z)$.......................................................................... 32
3. The D-R homomorphism theorem................................................................................. 33
3.1. Eigenvectors of D and R................................................................................. 35
4. The D-R homomorphism theorem for $D_D_0$ $\varsubsetneqq$ X.................. 35
5. $d_0$-topology................................................................................................................... 38
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Seria
Rozprawy Matematyczne tom/nr w serii: 184
Liczba stron
72
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLXXXIV
Daty
wydano
1981
Twórcy
autor
Bibliografia
• [1] Berg, L., Operatorenrechnung, I. Algebraische Methoden, Berlin 1972.
• [2] Berg, L., Anfangswertprobleme für zusammengesetzte Operatoren, Wiss. Zeitschr. d. Univ. Rostock-24 Jahrg. (1975), Math.-Nattirw. Reihe, Heft 10, pp. 1227-1230.
• [3] Bourbaki, N., Topologie générale, III éd., Paris 1961.
• [4] Jacobson, N., Lectures in abstract algebra, Princeton 1951, 1953, 1964.
• [5] Nashed, Z., Generalized inverses and applications, New York 1976.
• [6] Przeworska-Rolewicz, D. and S. Rolewicz, Equations in linear spaces, Warszawa 1968.
• [7] Przeworska-Rolewicz, D., Algebraic derivative and abstract differential equations, Ann. d. Acad. Bras. d. Ciencias 42 (1970), pp. 403-409.
• [8] Przeworska-Rolewicz, D., Algebraic theory of right invertible operators, Studia Math. 48 (1973), pp. 129-144.
• [9] Przeworska-Rolewicz, D., Admissible initial operators for superpositions of right invertible operators, Ann. Pol. Math. 32 (1976), pp. 113-120 (Polish version published 1974 in Biuletyn WAT rok 23, nr 7, pp. 23-30).
• [10] Tasche, M., Algebraische Operatorenrechnung für einen rechtsinvertierbaren Operator, Wiss. Zeitschr. d. Univ. Rostock-23 Jahrg. (1974), Math.-Naturw. Reihe, Heft 10, pp. 735-744.
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