### Abstract

Consider Krein spaces U and Y and let H_{k} and K_{k} be regular subspaces of U and Y, respectively, such that H_{k}⊂H_{k+1} and K_{k}⊂K_{k+1} (kϵN). For each kϵN, let A_{k}:H_{k}→K_{k} be a contraction. We derive necessary and sufficient conditions for the existence of a contraction B:U→Y such that B/H_{k}=A_{k}. Some interesting results are proved along the way.

Original language | English |
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Article number | 5178454 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 2018 |

DOIs | |

Publication status | Published - Jan 1 2018 |

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### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

**An Extension Theorem for a Sequence of Krein Space Contractions.** / Wanjala, Gerald.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - An Extension Theorem for a Sequence of Krein Space Contractions

AU - Wanjala, Gerald

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Consider Krein spaces U and Y and let Hk and Kk be regular subspaces of U and Y, respectively, such that Hk⊂Hk+1 and Kk⊂Kk+1 (kϵN). For each kϵN, let Ak:Hk→Kk be a contraction. We derive necessary and sufficient conditions for the existence of a contraction B:U→Y such that B/Hk=Ak. Some interesting results are proved along the way.

AB - Consider Krein spaces U and Y and let Hk and Kk be regular subspaces of U and Y, respectively, such that Hk⊂Hk+1 and Kk⊂Kk+1 (kϵN). For each kϵN, let Ak:Hk→Kk be a contraction. We derive necessary and sufficient conditions for the existence of a contraction B:U→Y such that B/Hk=Ak. Some interesting results are proved along the way.

UR - http://www.scopus.com/inward/record.url?scp=85044104770&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044104770&partnerID=8YFLogxK

U2 - 10.1155/2018/5178454

DO - 10.1155/2018/5178454

M3 - Article

VL - 2018

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

M1 - 5178454

ER -