复Hilbert空间单位球上一类新的Roper-Suffridge算子

Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (4): 637-646.

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A New Roper-Suffridge Extension Operator on the Unit Ball in Hilbert Spaces

Xia Hongchuan¹, Liu Hao², Zhong Chunping³

1 College of Mathematics and Statistics, Xinyang Normal University, Henan Xinyang 464000;
2 College of Mathematics and Statistics, Henan University, Henan Kaifeng 475001;
3 School of Mathematical Sciences, Xiamen University, Fujian Xiamen 361005

Received:2016-10-21 Revised:2017-03-17 Online:2017-08-26 Published:2017-08-26
Supported by:
Supported by the NSFC (11571288, 11671330, 11271359, 11471098) and the Nanhu Scholars Program for Young Scholars of XYNU

Abstract

Abstract:

In this paper, we construct a new Roper-Suffridge extension operator

on the unit ball B in complex Hilbert space X, where dim X ≥ n, f is a normalized locally biholomorphic function on the unit disc D, {e_j∈X,j=1,2,…n} is a series of orthogonal unit vectors in X. Under some special conditions of β_j, we prove the operator can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of order α on the unit ball B, respectively.

Key words: Roper-Suffridge operator, Biholomorphic mappings, Hilbert spaces

CLC Number:

O174.56

Xia Hongchuan, Liu Hao, Zhong Chunping. A New Roper-Suffridge Extension Operator on the Unit Ball in Hilbert Spaces[J].Acta mathematica scientia,Series A, 2017, 37(4): 637-646.

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References

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A New Roper-Suffridge Extension Operator on the Unit Ball in Hilbert Spaces

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