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Definition df-bdop 27867
Description: Define the set of bounded linear Hilbert space operators. (See df-hosum 27755 for definition of operator.) (Contributed by NM, 18-Jan-2006.) (New usage is discouraged.)
Assertion
Ref Expression
df-bdop BndLinOp = {𝑡 ∈ LinOp ∣ (normop𝑡) < +∞}

Detailed syntax breakdown of Definition df-bdop
StepHypRef Expression
1 cbo 26971 . 2 class BndLinOp
2 vt . . . . . 6 setvar 𝑡
32cv 1473 . . . . 5 class 𝑡
4 cnop 26968 . . . . 5 class normop
53, 4cfv 5694 . . . 4 class (normop𝑡)
6 cpnf 9830 . . . 4 class +∞
7 clt 9833 . . . 4 class <
85, 6, 7wbr 4481 . . 3 wff (normop𝑡) < +∞
9 clo 26970 . . 3 class LinOp
108, 2, 9crab 2804 . 2 class {𝑡 ∈ LinOp ∣ (normop𝑡) < +∞}
111, 10wceq 1474 1 wff BndLinOp = {𝑡 ∈ LinOp ∣ (normop𝑡) < +∞}
Colors of variables: wff setvar class
This definition is referenced by:  elbdop  27885  hhbloi  27927
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