Weak and strong convergence of operator sequence
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Let $|e|leq1$ such that $eneq0$, we define the lineal operator $F_e: C^1([-1,1],R)rightarrow R $ as $$ F_e x(t) =frac{x(e) - x(-e)} {2 e} . $$
I need to know if the sequence of operators ${{F_e} }_e$ converges weakly and/or strongly to some operator as $erightarrow0$.
I suspect that limit could be $x'(0)$ but Idk how to prove it or disprove it.
functional-analysis operator-theory weak-convergence strong-convergence
asked Jan 25 at 3:39
NeuphoriaNeuphoria
283
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add a comment |
$begingroup$
Let $|e|leq1$ such that $eneq0$, we define the lineal operator $F_e: C^1([-1,1],R)rightarrow R $ as $$ F_e x(t) =frac{x(e) - x(-e)} {2 e} . $$
I need to know if the sequence of operators ${{F_e} }_e$ converges weakly and/or strongly to some operator as $erightarrow0$.
I suspect that limit could be $x'(0)$ but Idk how to prove it or disprove it.
functional-analysis operator-theory weak-convergence strong-convergence
asked Jan 25 at 3:39
NeuphoriaNeuphoria
283
$endgroup$
1
$begingroup$
math.meta.stackexchange.com/questions/5020/…
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– Lord Shark the Unknown
Jan 25 at 4:05
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Thank you, that will help me to learn the basics.
$endgroup$
– Neuphoria
Jan 25 at 10:26
add a comment |
$begingroup$
Let $|e|leq1$ such that $eneq0$, we define the lineal operator $F_e: C^1([-1,1],R)rightarrow R $ as $$ F_e x(t) =frac{x(e) - x(-e)} {2 e} . $$
I need to know if the sequence of operators ${{F_e} }_e$ converges weakly and/or strongly to some operator as $erightarrow0$.
I suspect that limit could be $x'(0)$ but Idk how to prove it or disprove it.
functional-analysis operator-theory weak-convergence strong-convergence
asked Jan 25 at 3:39
NeuphoriaNeuphoria
283
$endgroup$
Let $|e|leq1$ such that $eneq0$, we define the lineal operator $F_e: C^1([-1,1],R)rightarrow R $ as $$ F_e x(t) =frac{x(e) - x(-e)} {2 e} . $$
I need to know if the sequence of operators ${{F_e} }_e$ converges weakly and/or strongly to some operator as $erightarrow0$.
I suspect that limit could be $x'(0)$ but Idk how to prove it or disprove it.
functional-analysis operator-theory weak-convergence strong-convergence
functional-analysis operator-theory weak-convergence strong-convergence
asked Jan 25 at 3:39
NeuphoriaNeuphoria
283
asked Jan 25 at 3:39
NeuphoriaNeuphoria
283
edited Jan 25 at 10:33
Neuphoria
asked Jan 25 at 3:39
NeuphoriaNeuphoria
283
asked Jan 25 at 3:39
NeuphoriaNeuphoria
283
asked Jan 25 at 3:39
NeuphoriaNeuphoria
283
283
1
$begingroup$
math.meta.stackexchange.com/questions/5020/…
$endgroup$
– Lord Shark the Unknown
Jan 25 at 4:05
$begingroup$
Thank you, that will help me to learn the basics.
$endgroup$
– Neuphoria
Jan 25 at 10:26
add a comment |
1
$begingroup$
math.meta.stackexchange.com/questions/5020/…
$endgroup$
– Lord Shark the Unknown
Jan 25 at 4:05
$begingroup$
Thank you, that will help me to learn the basics.
$endgroup$
– Neuphoria
Jan 25 at 10:26
1
1
$begingroup$
math.meta.stackexchange.com/questions/5020/…
$endgroup$
– Lord Shark the Unknown
Jan 25 at 4:05
$begingroup$
math.meta.stackexchange.com/questions/5020/…
$endgroup$
– Lord Shark the Unknown
Jan 25 at 4:05
$begingroup$
Thank you, that will help me to learn the basics.
$endgroup$
– Neuphoria
Jan 25 at 10:26
$begingroup$
Thank you, that will help me to learn the basics.
$endgroup$
– Neuphoria
Jan 25 at 10:26
add a comment |
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1
$begingroup$
math.meta.stackexchange.com/questions/5020/…
$endgroup$
– Lord Shark the Unknown
Jan 25 at 4:05
$begingroup$
Thank you, that will help me to learn the basics.
$endgroup$
– Neuphoria
Jan 25 at 10:26