On a class of unitary operators on the Bergman space of the right half plane

Namita DAS; Jitendra Kumar BEHERA

Makale detayları

On a class of unitary operators on the Bergman space of the right half plane

Yazarlar:

Namita DAS | Jitendra Kumar BEHERA

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 2, pp.471-486

Belge Tipi:

Makale

Yayın Tarihi:

3/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745909

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

In this paper, we introduce a class of unitary operators defined on the Bergman space L2a(C+)La2(C+)L_a^2(\mathbb{C}_+) of the right half plane C+C+\mathbb{C}_+ and study certain algebraic properties of these operators. Using these results, we then show that a bounded linear operator SSS from L2a(C+)La2(C+)L_a^2(\mathbb{C}_+) into itself commutes with all the weighted composition operators Wa,a∈DWa,a∈DW_a, a \in \mathbb{D} if and only if ˜S(w)=⟨Sb¯¯¯¯w,b¯¯¯¯w⟩,w∈C+S~(w)=⟨Sbw¯,bw¯⟩,w∈C+\widetilde{S}(w)=\langle Sb_{\overline{w}},b_{\overline{w}}\rangle, w \in \mathbb{C}_+  satisfies a certain averaging condition. Here for a=c+id∈D,f∈L2a(C+),Waf=(f∘ta)M′M′∘ta,Ms=1−s1+s,ta(s)=−ids+(1−c)(1+c)s+ida=c+id∈D,f∈La2(C+),Waf=(f∘ta)M′M′∘ta,Ms=1−s1+s,ta(s)=−ids+(1−c)(1+c)s+ida=c+id \in \mathbb{D}, f \in L_a^2(\mathbb{C}_+), W_af=(f \circ t_a) \frac{M^{\prime}}{M^{\prime} \circ t_a}, Ms=\frac{1-s}{1+s}, t_a(s)=\frac{-ids +(1-c)}{(1+c)s + id}, and b¯¯¯¯w(s)=1√π1+w1+¯¯¯¯w2Rew(s+w)2,w=M¯¯¯a,s∈C+.bw¯(s)=1π1+w1+w¯2Rew(s+w)2,w=Ma¯,s∈C+.b_{\overline{w}}(s)=\frac{1}{\sqrt{\pi}} \frac{1+w}{1+\overline{w}} \frac{2 \mbox {Re} w}{(s+w)^2}, w=M\overline {a}, s \in \mathbb{C}_+. Some applications of these results are also discussed.

Makale detayları

On a class of unitary operators on the Bergman space of the right half plane

Yazarlar: Namita DAS | Jitendra Kumar BEHERA

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2018 Vol.42 Issue 2, pp.471-486

Belge Tipi: Makale

Yayın Tarihi: 3/2018

Belge Dili: Türkçe

Document ID (Org No.): 2000745909

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Namita DAS | Jitendra Kumar BEHERA

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 2, pp.471-486

Belge Tipi:

Makale

Yayın Tarihi:

3/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745909

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098