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Proof ⇒) Suppose T X → Y is a bounded linear operator, then kTxk ≤ kTkkxk, which means that if x is bounded then Tx should also bounded ⇐) Choose the closed unit ball B = B1(0) ⊂ X, then B is bounded so α = sup x∈B kTxk < ∞ Since ∀x ∈ X, x kxk ∈ B, so T x kxk ≤ α ⇒ kTxk ≤ αkxk It implies that T is bounded III. 1716 · Upgrade to Pro — share decks privately, control downloads, hide ads and more 0 d e f f u n c 1 ( ) f o r i i n r a n g e ( 5 0 0 0 0 ) # A ç õ e s e x t r a s n s 0 = n s 0 Retorna se o processo está vivo d a e m o n Indicador se o processo é do tipo daemon API idêntica à t h r e a d i n g T h. Proof ⇒) Suppose T X → Y is a bounded linear operator, then kTxk ≤ kTkkxk, which means that if x is bounded then Tx should also bounded ⇐) Choose the closed unit ball B = B1(0) ⊂ X, then B is bounded so α = sup x∈B kTxk < ∞ Since ∀x ∈ X, x kxk ∈ B, so T x kxk ≤ α ⇒ kTxk ≤ αkxk It implies that T is bounded III. · 40 C M Hoffmann and J E Hopcroft Model generation and modification for dynamic systems from geometric data In B Ravani, editor, CAD Based Programming for Sensory Robots, pages 481–492, Springer NATO ASI Series F50, 19.
