Aims: We are using the Arecibo Legacy Fast ALFA survey (ALFALFA), which is covering 17% of the sky at 21 cm, to study the HI content of Early-Type galaxies (ETG) in an unbiased way. The aim is to get an overall picture of the hot, warm and cold ISM of ETG, as a function of galaxy mass and environment, to understand its origin and fate, and to relate it to the formation and evolution history of these objects. Methods: This paper deals with the first part of our study, which is devoted to the 8-16 deg. declination strip in the Virgo cluster. In this sky region, using the Virgo Cluster Catalogue (VCC), we have defined an optical sample of 939 ETG, 457 of which are brighter than the VCC completeness limit at B_T=18.0. We have correlated this optical sample with the catalogue of detected HI sources from ALFALFA. Results: Out of the 389 ETG from the VCC with B_T<=18.0, outside the 1 deg. region of poor HI detection around M87, and corrected for background contamination of VCC galaxies without a known radial velocity, only 9 galaxies (2.3%) are detected in HI with a completeness limit of 3.5 and 7.6 x 10^7 Mo of HI for dwarf and giant ETG, respectively. In addition 4 VCC ETG with fainter magnitudes are also detected. Our HI detection rate is lower than previously claimed. The majority of the detected ETG appear to have peculiar morphology and to be located near the edges of the Virgo cluster. Conclusions: Our preliminary conclusion is that cluster ETG contain very little neutral gas, with the exceptions of a few peculiar dwarf galaxies at the edge of the ETG classification and of very few larger ETG, where the cold gas could have a recent external origin.
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