Definition df-bdop 10048

Description: Define the set of bounded linear Hilbert space operators. (See df-hosum 9782 for definition of operator.)

Assertion

Ref	Expression
df-bdop	|- BndLinOp = (LinOp i^i {t | (t:H~-->H~ /\ (normop` t) < +oo)})

Detailed syntax breakdown of Definition df-bdop

Step	Hyp	Ref	Expression
1		cbo 9092	. 2 class BndLinOp
2		clo 9091	. . 3 class LinOp
3		chil 9063	. . . . . 6 class H~
4		vt	. . . . . . 7 set t
5	4	cv 991	. . . . . 6 class t
6	3, 3, 5	wf 3259	. . . . 5 wff t:H~-->H~
7		cnop 9089	. . . . . . 7 class normop
8	5, 7	cfv 3263	. . . . . 6 class (normop` t)
9		cpnf 5637	. . . . . 6 class +oo
10		clt 5640	. . . . . 6 class <
11	8, 9, 10	wbr 2692	. . . . 5 wff (normop` t) < +oo
12	6, 11	wa 221	. . . 4 wff (t:H~-->H~ /\ (normop` t) < +oo)
13	12, 4	cab 1505	. . 3 class {t | (t:H~-->H~ /\ (normop` t) < +oo)}
14	2, 13	cin 2098	. 2 class (LinOp i^i {t | (t:H~-->H~ /\ (normop` t) < +oo)})
15	1, 14	wceq 992	1 wff BndLinOp = (LinOp i^i {t | (t:H~-->H~ /\ (normop` t) < +oo)})

This definition is referenced by:  dfbdop2 10066

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