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Definition df-hosum 22108
Description: Define the sum of two Hilbert space operators. Definition of [Beran] p. 111. (Contributed by NM, 9-Nov-2000.) (New usage is discouraged.)
Assertion
Ref Expression
df-hosum  |-  +op  =  ( f  e.  ( ~H  ^m  ~H ) ,  g  e.  ( ~H  ^m  ~H )  |->  ( x  e.  ~H  |->  ( ( f `  x
)  +h  ( g `
 x ) ) ) )
Distinct variable group:    f, g, x

Detailed syntax breakdown of Definition df-hosum
StepHypRef Expression
1 chos 21464 . 2  class  +op
2 vf . . 3  set  f
3 vg . . 3  set  g
4 chil 21445 . . . 4  class  ~H
5 cmap 6726 . . . 4  class  ^m
64, 4, 5co 5778 . . 3  class  ( ~H 
^m  ~H )
7 vx . . . 4  set  x
87cv 1618 . . . . . 6  class  x
92cv 1618 . . . . . 6  class  f
108, 9cfv 4659 . . . . 5  class  ( f `
 x )
113cv 1618 . . . . . 6  class  g
128, 11cfv 4659 . . . . 5  class  ( g `
 x )
13 cva 21446 . . . . 5  class  +h
1410, 12, 13co 5778 . . . 4  class  ( ( f `  x )  +h  ( g `  x ) )
157, 4, 14cmpt 4037 . . 3  class  ( x  e.  ~H  |->  ( ( f `  x )  +h  ( g `  x ) ) )
162, 3, 6, 6, 15cmpt2 5780 . 2  class  ( f  e.  ( ~H  ^m  ~H ) ,  g  e.  ( ~H  ^m  ~H )  |->  ( x  e. 
~H  |->  ( ( f `
 x )  +h  ( g `  x
) ) ) )
171, 16wceq 1619 1  wff  +op  =  ( f  e.  ( ~H  ^m  ~H ) ,  g  e.  ( ~H  ^m  ~H )  |->  ( x  e.  ~H  |->  ( ( f `  x
)  +h  ( g `
 x ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  hosmval  22113
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