Mean Ergodic Weighted Composition Operator 饾潃饾應饾潒 on Bloch Space

Document Type : research paper

Authors

1 Department of Mathematics, Islamic Azad University, Shiraz Branch, Shiraz, Iran

2 faculty membrer of Islamic Azad University, Shiraz branch

Abstract

Investigating the mean ergodicity of composition operators on various Banach Spaces has always been of interest to mathematicians and many authors studied this topics intensively, in many different spaces, such as, the space of all holomorphic functions on unit disk, Hardy space and Bloch space. In this paper, for a self map of the unit disk, φ and λ∈鈩, we consider weighted composition operator, (λ饾惗φ)饾憮=λ饾憮饾憸φ , for every 饾憮 in Bloch space and Little Bloch space and inquiry the conditions under which the weighted composition operator 饾渾饾惗饾湋, is mean ergodic or uniformly mean ergodic on the Bloch and Little Bloch Space. In fact, we will show, if |λ|>1,饾渾饾惗饾湋, cannot be power bounded, mean ergodic or uniformly mean ergodic, in contrast, if |λ|<1, 饾渾饾惗饾湋, is always power bounded, mean ergodic or uniformly mean ergodic. In the case, |λ|=1, we will see that it depends directly to the Denjoy-Wolff point of 饾湋.

Keywords


Article Title [賮丕乇爻蹖]

毓賲賱诏乇 鬲乇讴蹖亘蹖 賵夭賳 丿丕乇 饾潃饾應饾潒 丕乇诏賵丿蹖讴 賲蹖丕賳诏蹖賳 丿乇 賮囟丕蹖 亘賱賵趩

Authors [賮丕乇爻蹖]

  • 賮禺乇丕賱丿蹖賳 賮賱丕丨鬲 1
  • 夭賴乇丕 讴賲丕賱蹖 2
1 诏乇賵賴 乇蹖丕囟蹖貙 賵丕丨丿 卮蹖乇丕夭貙 丿丕賳卮诏丕賴 丌夭丕丿 丕爻賱丕賲蹖貙 卮蹖乇丕夭貙 丕蹖乇丕賳
2 诏乇賵賴 乇蹖丕囟蹖貙 賵丕丨丿 卮蹖乇丕夭貙 丿丕賳卮诏丕賴 丌夭丕丿 丕爻賱丕賲蹖貙 卮蹖乇丕夭貙 丕蹖乇丕賳
Abstract [賮丕乇爻蹖]

亘乇乇爻蹖 毓賲賱诏乇賴丕蹖 鬲乇讴蹖亘蹖 丕乇诏賵丿蹖讴 賲蹖丕賳诏蹖賳 丿乇 賮囟丕賴丕蹖 賲鬲賳賵毓 亘丕賳丕禺 賴賲賵丕乇賴 賲賵乇丿 毓賱丕賯賴 乇蹖丕囟蹖丿丕賳丕賳 亘賵丿賴 丕爻鬲 賵 亘爻蹖丕乇蹖 丕夭 賲賵賱賮丕賳 丿乇 爻丕賱賴丕蹖 丕禺蹖乇 貙 丕蹖賳 賲爻卅賱賴 乇丕 亘胤賵乇 丿賯蹖賯 丿乇 賮囟丕賴丕蹖 賲禺鬲賱賮貙 丕夭 噩賲賱賴 賮囟丕蹖 鬲賵丕亘毓 鬲丨賱蹖賱蹖 丿乇 丿蹖爻讴 賵丕丨丿貙 賮囟丕蹖 賴丕乇丿蹖 賵 賮囟丕蹖 亘賱賵趩貙 賲賵乇丿 亘乇乇爻蹖 賵 賵丕讴丕賵蹖 賯乇丕乇丿丕丿賴 丕賳丿.
丿乇 丕蹖賳 賲賯丕賱賴 亘乇丕蹖 蹖讴 禺賵丿賳诏丕卮鬲 φ 丕夭 丿蹖爻讴 賵丕丨丿 賵 λ∈鈩 貙 毓賲賱诏乇 鬲乇讴蹖亘蹖 賵夭賳丿丕乇貙 (λ饾惗φ)饾憮=λ饾憮饾憸φ 亘乇丕蹖 賴乇 饾憮 丿乇 賮囟丕蹖 亘賱賵趩 賵 賮囟丕蹖 亘賱賵趩 讴賵趩讴 丿乇 賳馗乇 賲蹖 诏蹖乇蹖賲 賵 亘賴 亘乇乇爻蹖 卮乇丕蹖胤蹖 賲蹖 倬乇丿丕夭蹖賲 讴賴 胤蹖 丌賳 毓賲賱诏乇 鬲乇讴蹖亘蹖 賵夭 賳 丿丕乇 饾渾饾惗饾湋 貙 乇賵蹖 賮囟丕賴丕蹖 亘丕賳丕禺 亘賱賵趩 賵 亘賱賵趩 讴賵趩讴貙 丕乇诏賵丿蹖讴 賲蹖丕賳诏蹖賳 賵 亘賴 胤賵乇 蹖讴賳賵丕禺鬲 丕乇诏賵丿蹖讴 賲蹖丕賳诏蹖賳 賲蹖 亘丕卮丿. 丿乇 賵丕賯毓 賳卮丕賳 賲蹖 丿賴蹖賲 丕诏乇 |λ|>1 貙 λ饾惗φ 賳賲蹖 鬲賵丕賳丿 讴乇丕 賳 丿丕乇 鬲賵丕賳蹖 丕乇诏賵丿蹖讴 賲蹖丕賳诏蹖賳 賵 亘賴 胤賵乇 蹖讴賳賵丕禺鬲 丕乇诏賵丿蹖讴 賲蹖丕賳诏蹖賳 亘丕卮丿 賵 丿乇 賲賯丕亘賱 丕诏乇 |λ|<1 貙 λ饾惗φ 賴賲賵丕乇賴 讴乇丕賳 丿丕乇 鬲賵丕賳蹖 丕 乇诏賵丿蹖讴 賲蹖丕賳诏蹖賳 賵 亘賴 胤賵乇 蹖讴賳賵丕禺鬲 丕乇诏賵丿蹖讴 賲蹖丕賳诏蹖賳 賲蹖 亘丕卮丿 賵 丿乇 丨丕賱鬲 |λ|=1 貙 禺賵丕賴蹖賲 丿蹖丿 讴賴 丕蹖賳 賲賵囟賵毓 丕乇鬲亘丕胤 賲爻鬲賯蹖賲蹖 亘丕 賳賯胤賴 丿賳噩賵蹖 - 賵賱賮 饾湋 丿丕乇丿.

Keywords [賮丕乇爻蹖]

  • 毓賲賱诏乇 鬲乇讴蹖亘蹖 賵夭賳鈥屫ж
  • 毓賲賱诏乇 丕乇诏賵丿蹖讴 賲蹖丕賳诏蹖賳
  • 賳賯胤賴 丿賳噩賵蹖-賵賱賮
  • 賮囟丕蹖 亘賱賵趩
 
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