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Definition df-bdop 28829
Description: Define the set of bounded linear Hilbert space operators. (See df-hosum 28717 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 27933 . 2 class BndLinOp
2 vt . . . . . 6 setvar 𝑡
32cv 1522 . . . . 5 class 𝑡
4 cnop 27930 . . . . 5 class normop
53, 4cfv 5926 . . . 4 class (normop𝑡)
6 cpnf 10109 . . . 4 class +∞
7 clt 10112 . . . 4 class <
85, 6, 7wbr 4685 . . 3 wff (normop𝑡) < +∞
9 clo 27932 . . 3 class LinOp
108, 2, 9crab 2945 . 2 class {𝑡 ∈ LinOp ∣ (normop𝑡) < +∞}
111, 10wceq 1523 1 wff BndLinOp = {𝑡 ∈ LinOp ∣ (normop𝑡) < +∞}
Colors of variables: wff setvar class
This definition is referenced by:  elbdop  28847  hhbloi  28889
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