split line based on space and delete the second part

I have a big file

>fid|29290408|locus|VBIEntCas2262_0001|   Phosphoglycolate phosphatase (EC 3.1.3.18)   [Enterococcus casseliflavus EC20]
gtgagaaagaaagtactttttgatttagatggaacgatcattgattcgagtgaaggaatc
tatggatcgattcaatatgcgatggaaaaaatgggaaaagagcaattagcgcaagacgta
ctgcggagctttgtggggccgcctttgattgaatccttccgtggcttgggcttcgatgaa
>fid|29290410|locus|VBIEntCas2262_0002|   hypothetical protein   [Enterococcus casseliflavus EC20]
atgatcggcgaacgttttttgatcacaccgatcgacgaaccgttagacccatacaatgag
ttagtctcaagcaatcagtttactttctttacatcaacctatgatcaaatgttcttgact
ggtcatctgattctagatgttcacccaacttcaggaactttgattttgaaaaacgaaagc
ggctatttggataccaatcttttattggaatcctctccacagttaaaacaaacgaatgcg
>fid|29290414|locus|VBIEntCas2262_0004|   FIG00630550: hypothetical protein   [Enterococcus casseliflavus EC20]
atgaagcgtgttgcagaaaactatttggttgttttttcgattcttttgctgattatatgg
ctaggcttgatccaagtgaaagaatattcgcaagaagtagccctgtcgatcatttacttt

I need to split each line beginning with ">" based on the space, retaining in the new file only the part before the spaces, with the following lines.

So the file I need should be:

>fid|29290408|locus|VBIEntCas2262_0001|
gtgagaaagaaagtactttttgatttagatggaacgatcattgattcgagtgaaggaatc
tatggatcgattcaatatgcgatggaaaaaatgggaaaagagcaattagcgcaagacgta
ctgcggagctttgtggggccgcctttgattgaatccttccgtggcttgggcttcgatgaa

an so on.

the number of lines following the header (starting with >) is not fixed.

How could I do?