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Matrix Valued Truncated Toeplitz Operators

Thesis Info

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Author

Khan, Rewayat.

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/9421/1/Rewayat_Khan_Maths_2018_GCU_lahore_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726622571

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This thesis contains results about the matrix valued truncated Toeplitz operators (MTTO''s) de ned on the model space K= H2 H2(E), with axed pure inner function and E an arbitrary Hilbert space. The class of MTTO''s is denoted by T (K ). In the main work of this thesis we shall concern with the extension of some of the results obtained in the scalar case by D. Sarason in [27]. After gathering together the mathematical preliminaries of this work in Chapter 1, in Chapter 2 we shall present the most important properties of the model spaces Kand some very important operators Sand S in T (K ). The main object of this thesis is the study of the matrix generalization of the truncated Toeplitz operators introduced in [27]; a more recent presentation is [17]. This will be the content of Chapter 3, 4, 5. Finally, in Chapter 6 the preceding theory is applied to initiate the study ofnite rank operators in T (K ).
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دھی دی خوشی

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پرانے زمانے دی گل اے کہ کسے ملک اتے اک بہت رحم دل بادشاہ حکومت کردا سی۔ اپنی رعایا دا خیال رکھدا تے اوہناں نوں ودھ توں ودھ سہولتاں دیون دی کوشش کردا۔ پر ربّ دا کرنا انج ہویا کہ ویاہ دے ویہہ سال بعد وی اوس گھر کوئی اولاد نہ ہوئی۔ ایس کر کے اوہ بہت پریشان رہندا سی۔ اوس کئی حکیماں توں اپنا تے ملکہ دا علاج وی کروایا ربّ نے اوس نوں اولاد دی نعمت عطا نہ کیتی۔

اک دن اوہ اکلا اپنے محل دے بوہے تے کھڑا بالاں نوں کھیڈ دا ویکھ رہیا سی۔ اوہدیاں اکھاں وچ اولاد نہ ہوون پاروں اتھرو آ گئے۔ اچانک بادشاہ نوں کھڑا ویکھ کے اک فقیر اوہدے کول آ گیا تے افسردہ ہوون دی وجہ پچھی۔ بادشاہ نے دسیا کہ بابا میرے کول اولاد نئیں اے۔ بابے نے آکھیا میں کئی دناں دا بھکھا آں۔ توں مینوں روٹی کھلا دے۔ ربّ تینوں اولاد دیوے گا۔ بادشاہ اوس فقیر نوں بڑے ادب نال لے کے محل اندر آیا تے شاہی برتناں وچ اوس نوں کھانا پیش کیتا۔ جان لگیا بادشاہ نے نذرانے دے طور تے کجھ پیسے دے دتے۔ فقیر اولاد دی دُعا دیندے ہوئے چلا گیا۔

ربّ نے فقیر دی دُعا قبول کر لئی تے اک سال بعد ربّ نے بادشاہ نوں اک سوہنی دھی دا تحفہ دتا۔ اوہ تے ملکہ دھی دی آمد تے بہت خوش سن۔ جدوں رعایا نوں شہزادی دا پتہ لگا تاں اوہ وی بہت خوش ہوئی۔ بادشاہ نے سارے ملک وچ خیرات ونڈی۔ ایس توں غریباں نوں کھانا کھاون دا وی انتظام کیتا۔ خود اک وڈی دعوت دا انتظام اپنے شہر وچ کیتا۔ مقررہ تاریخ تے بہت سارے لوک ایس دعوت وچ آئے اوہناں شہزادی نال کپڑے، کھڈو نے تے...

المحاسبة الإدارية فـي القـرآن الكـريم مـن خلال قصة يوسـف عـليه السلام: دراسة تأصيلية مقارنة

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Dynamics of Social Expenditures, Poverty Reduction and Pro-Poor Growth in Pakistan

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