Morteza RAHMANI.On Some Properties of $c$-Frames[J].数学研究及应用,2017,37(4):466~476
On Some Properties of $c$-Frames
On Some Properties of $c$-Frames
投稿时间:2016-04-30  最后修改时间:2017-03-29
DOI:10.3770/j.issn:2095-2651.2017.04.008
中文关键词:  Banach space  Hilbert space  frame  $c$-frame  Parseval $c$-frame  Bochner measurable
英文关键词:Banach space  Hilbert space  frame  $c$-frame  Parseval $c$-frame  Bochner measurable
基金项目:
作者单位
Morteza RAHMANI Young Researchers and Elite Club, Ilkhchi Branch, Islamic Azad University, Ilkhchi, Iran 
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中文摘要:
      In this paper we discuss about $c$-frames, namely continuous frames. Since, $c$-frames are generalizations of discrete frames, we generalize some results of discrete frames to continuous version. We explain some results about relations of projections in Hilbert spaces and $c$-frames to characterize these frames. Also, we will specify (precisely) the synthesis and frame operators of Bochner integrable $c$-frames. Finally, we classify Hilbert-Schmidt operators by $c$-frames and express some new identities for Parseval $c$-frames.
英文摘要:
      In this paper we discuss about $c$-frames, namely continuous frames. Since, $c$-frames are generalizations of discrete frames, we generalize some results of discrete frames to continuous version. We explain some results about relations of projections in Hilbert spaces and $c$-frames to characterize these frames. Also, we will specify (precisely) the synthesis and frame operators of Bochner integrable $c$-frames. Finally, we classify Hilbert-Schmidt operators by $c$-frames and express some new identities for Parseval $c$-frames.
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