### Citations

542 | Constructive Analysis
- Bishop, Bridges
- 1985
(Show Context)
Citation Context ..., we deal with compact linear mappings of a normed linear space, within the framework of Bishop's constructive mathematics; we assume familiarity with the foundations of constructive mathematics; see =-=[1, 2, 3, 4]-=-. Although constructive investigations of compact linear mappings could be found in [2, Chapter 7, Problem 41-43], [4, Chapter 2], [5], some elementary classical facts on compact linear mappings have ... |

79 |
1985]: Constructive Mathematics
- Bishop, Bridges
(Show Context)
Citation Context ..., we deal with compact linear mappings of a normed linear space, within the framework of Bishop's constructive mathematics; we assume familiarity with the foundations of constructive mathematics; see =-=[1, 2, 3, 4]-=-. Although constructive investigations of compact linear mappings could be found in [2, Chapter 7, Problem 41-43], [4, Chapter 2], [5], some elementary classical facts on compact linear mappings have ... |

43 |
Constructive Functional Analysis
- Bridges
- 1979
(Show Context)
Citation Context ..., we deal with compact linear mappings of a normed linear space, within the framework of Bishop's constructive mathematics; we assume familiarity with the foundations of constructive mathematics; see =-=[1, 2, 3, 4]-=-. Although constructive investigations of compact linear mappings could be found in [2, Chapter 7, Problem 41-43], [4, Chapter 2], [5], some elementary classical facts on compact linear mappings have ... |

23 |
Foundations of constructive analysis (McGraw{Hill
- Bishop
- 1967
(Show Context)
Citation Context |

8 |
Constructive compact operators on a Hilbert space
- Ishihara
- 1991
(Show Context)
Citation Context ...y, the author proved this theorem. Let A and B be compact operators on a Hilbert space H and let C be an operator on H. Then A + B is compact, A* is compact, and if C* exists, then AC is compact; see =-=[6]-=-. Since the proof of the theorem depends on the geometric properties of Hilbert spaces, we cannot expect to generalize the theorem to arbitrary normed linear spaces in the same manner. In the sequel, ... |

3 |
Bounded linear mappings of finite rank
- Bridges, Calder, et al.
- 1981
(Show Context)
Citation Context ...ty with the foundations of constructive mathematics; see [1, 2, 3, 4]. Although constructive investigations of compact linear mappings could be found in [2, Chapter 7, Problem 41-43], [4, Chapter 2], =-=[5]-=-, some elementary classical facts on compact linear mappings have not been proved constructively; for example the compactness of the sum of compact linear mappings, which is classically proved by mean... |